tag:blogger.com,1999:blog-79413141052447724712024-03-12T19:06:06.862-07:00TANGENT (A direction to success)As the name suggests "TANGENT" which means direction.
A direction to success in Mathemetics
A subject which is fear for all. It has actually nothing to fear.
It is the only subject where you don't need to learn only understand and apply.
It can be made fun with games and also can be studied with music.
Unknownnoreply@blogger.comBlogger28125tag:blogger.com,1999:blog-7941314105244772471.post-25510978152446352302014-07-04T07:52:00.001-07:002014-07-04T07:52:28.117-07:001st STEP TOWARDS MY AIM TO BE DR. MEHAK CHAWLA NAGPAL<div dir="ltr" style="text-align: left;" trbidi="on">
Hi<br />
<br />
Back from my maternity leave...With a great news...<br />
My contribution in the field of Mathematics<br />
Introducing my first article in a journal....Journey towards the Phd degree starts<br />
<br />
Interested!!!!!!<br />
<br />
TOPIC: <b><i><span style="font-size: large;">On a new class of integrals involving Bessel functions of the first kind</span></i></b><br />
<div>
<br /></div>
<div>
Follow the Link</div>
<br />
http://www.ispacs.com/journals/cna/2014/cna-00216/article.pdf<br />
<br /></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-813239930881897712013-11-12T22:10:00.003-08:002013-11-12T22:10:53.698-08:00Answer to the puzzle<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="color: magenta; font-family: Georgia, Times New Roman, serif; font-size: large;"><b><i>The lines add up to 14 so,</i></b></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5yWsf7nMt8ojfLSA_OhhNNW9LBTqiSrM4P5gMRLtqJJgRBbckLmQt4ZDmxIUurP8ejpzJzXDWfHWM6sWG-AvewtpRcnF02F2vCUE1-Yc1CqUewPHNfmc6zIQh5PpIfRM9WrAJx8e83dY/s1600/untitled.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="344" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5yWsf7nMt8ojfLSA_OhhNNW9LBTqiSrM4P5gMRLtqJJgRBbckLmQt4ZDmxIUurP8ejpzJzXDWfHWM6sWG-AvewtpRcnF02F2vCUE1-Yc1CqUewPHNfmc6zIQh5PpIfRM9WrAJx8e83dY/s640/untitled.bmp" width="640" /></a></div>
<br /></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-88161700952850821132013-11-06T23:28:00.001-08:002013-11-06T23:28:57.935-08:00Puzzle for the day<div dir="ltr" style="text-align: left;" trbidi="on">
<b><i><span style="color: red; font-family: Georgia, Times New Roman, serif; font-size: large;">Put the numbers 1, 2,3 ,4 , 5, 6, 7 in the circles so that each straight line of three numbers adds up to the same total.</span></i></b><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwByVp8wW5hU8APNq92y19x9ZltouwMu3_KU6_eySms2BYGii3WdQmHYRfIfF-QG3iQ_yIQ8ZagWy0GFEaYNcyCcYVWoi7OmtbYbSIiTBT9DAuFknfSzabM-gy21p6wR2pYZ5lZDFbqHg/s1600/1.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="231" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwByVp8wW5hU8APNq92y19x9ZltouwMu3_KU6_eySms2BYGii3WdQmHYRfIfF-QG3iQ_yIQ8ZagWy0GFEaYNcyCcYVWoi7OmtbYbSIiTBT9DAuFknfSzabM-gy21p6wR2pYZ5lZDFbqHg/s400/1.bmp" width="400" /></a></div>
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<span style="font-family: Georgia, Times New Roman, serif; font-size: large;"><b><i><span style="color: red;">Hint 1</span><span style="color: magenta;">: As 7 is the largest of all numbers put it in the center circle.</span></i></b></span><br />
<span style="color: magenta; font-family: Georgia, Times New Roman, serif; font-size: large;"><b><i><br /></i></b></span>
<span style="font-family: Georgia, Times New Roman, serif; font-size: large;"><b><i><span style="color: red;">Hint 2</span><span style="color: magenta;">: Make pairs of the numbers that add up to 7 so that the total
is 14.</span></i></b></span><br />
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</div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-64564124655249563142013-10-13T00:30:00.000-07:002013-10-13T00:31:14.235-07:00COMPARISON OF WHOLE USING NUMBER LINE<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal">
<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;">See a number
line.....<o:p></o:p></span></i></b></span></div>
<div class="MsoNormal">
<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;"><br /></span></i></b></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidbefNsJE99x40gf-M_S3Qy-VZjVt6bU5yH8o-zz5Grp1bmw2dDSnZntNX9j8R19hnXwpusktzvYLpefQY7DdfWORa2tNi3Sm0x5XsEkw_xvDkWAlr4axmHDlu_xp9gKX3kEqd8MPu6zk/s1600/number+line.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><b><i><span style="color: #a64d79;"><img border="0" height="61" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidbefNsJE99x40gf-M_S3Qy-VZjVt6bU5yH8o-zz5Grp1bmw2dDSnZntNX9j8R19hnXwpusktzvYLpefQY7DdfWORa2tNi3Sm0x5XsEkw_xvDkWAlr4axmHDlu_xp9gKX3kEqd8MPu6zk/s320/number+line.png" width="320" /></span></i></b></a></div>
<div class="MsoNormal">
<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;">Observe on
this number line, what is the distance between the points 4 and 6?<o:p></o:p></span></i></b></span></div>
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<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;">It is 2
units, also 6 lies on the right of 4.<o:p></o:p></span></i></b></span></div>
<div class="MsoNormal">
<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;"><br /></span></i></b></span></div>
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<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;"> Can you tell the distance between 2 and 7?<o:p></o:p></span></i></b></span></div>
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<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;"><br /></span></i></b></span></div>
<div class="MsoNormal">
<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;">It is 5
units, also observe on the number line 7 lies on the right of 2.<o:p></o:p></span></i></b></span></div>
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<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;">So, 6 > 4
and 7 > 2. <o:p></o:p></span></i></b></span></div>
<div class="MsoNormal">
<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;"><br /></span></i></b></span></div>
<div class="MsoNormal">
<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;">So, if we
want to compare two whole numbers on a number line we can say that the number
which lies on the right is greater. As seen in the above examples 6 lies on the
right of 4 so 6 is greater and as 7 lies on the right of 2 so 7 is greater.<o:p></o:p></span></i></b></span></div>
<div class="MsoNormal">
<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;"><br /></span></i></b></span></div>
<div class="MsoNormal">
<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;">Similarly
for the same examples we can say that 4 lies on the left of 6 so, 4 is less
than 6.<o:p></o:p></span></i></b></span></div>
<div class="MsoNormal">
<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;"><br /></span></i></b></span></div>
<div class="MsoNormal">
<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;">If suppose
three whole numbers are to be compared using a number line say 32, 12, 21 then
first mark these numbers on the number line.<o:p></o:p></span></i></b></span></div>
<div class="MsoNormal">
<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;"><br /></span></i></b></span></div>
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<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;">Which number
can you say will be at the farthest right? We can see that 21 lie on the right
of 12, and 32 on the right of 21. <o:p></o:p></span></i></b></span></div>
<div class="MsoNormal">
<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;"><br /></span></i></b></span></div>
<div class="MsoNormal">
<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;">So, 32 >
21 > 12.<o:p></o:p></span></i></b></span></div>
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<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;">So, now if
you are given two large whole numbers say, 1053 and 2356, which number will lie
on the right?<o:p></o:p></span></i></b></span></div>
<div class="MsoNormal">
<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;"><br /></span></i></b></span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<span style="font-size: 16.0pt; line-height: 115%;"><b><i><span style="color: #a64d79;">As 2356 >
1053, hence 2356 lies on the right.</span></i></b><o:p></o:p></span></div>
</div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-3337479210065902332013-10-08T01:48:00.004-07:002013-10-08T01:48:43.621-07:00Time for the answer<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="color: #6fa8dc;"><i><b><span style="font-size: large;">The answer to riddle is 24 </span><span style="font-size: large;">= 2* 3* 4</span></b></i></span><br />
<span style="color: #6fa8dc; font-size: large;"><i><b><br /></b></i></span>
<span style="color: magenta; font-size: large;"><i><b>How did u find it?</b></i></span><br />
<span style="color: #6fa8dc; font-size: large;"><i><b><br /></b></i></span>
<span style="color: #0b5394; font-size: large;"><i><b>Write down all the numbers between 12 and 40 that are:</b></i></span><br />
<span style="color: #6fa8dc; font-size: large;"><i><b>13, 14, 15, 16, 17, 18, 19, 20 , 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39</b></i></span><br />
<span style="color: #6fa8dc; font-size: large;"><i><b><br /></b></i></span>
<span style="color: #0b5394; font-size: large;"><i><b>Now Clue 1 says it does not have 5 or 7 as the factor, so cancel out all numbers that have 5 or 7 as factor. we are left with:</b></i></span><br />
<span style="color: #6fa8dc; font-size: large;"><i><b>13, 16, 17, 18, 19, 22, 23, 24, 26, 27, 29, 31, 32, 33, 34, 36, 37, 38, 39</b></i></span><br />
<span style="color: #6fa8dc; font-size: large;"><i><b><br /></b></i></span>
<span style="color: #0b5394; font-size: large;"><i><b>Now, Clue 2: One of the factors is 4. Pick numbers with factor as 4.</b></i></span><br />
<span style="color: #6fa8dc; font-size: large;"><i><b><br /></b></i></span>
<span style="color: #6fa8dc; font-size: large;"><i><b>16, 24, 36</b></i></span><br />
<span style="color: #6fa8dc; font-size: large;"><i><b><br /></b></i></span>
<span style="color: #6fa8dc; font-size: large;"><i><b>Now out of these:</b></i></span><br />
<span style="color: #6fa8dc; font-size: large;"><i><b>16 = 4 * 4</b></i></span><br />
<span style="background-color: #a64d79; color: #6fa8dc; font-size: large;"><i><b>24 = 2 * 3 * 4</b></i></span><br />
<span style="color: #6fa8dc; font-size: large;"><i><b>36 = 6 * 6</b></i></span><br />
<span style="color: #6fa8dc; font-size: large;"><i><b><br /></b></i></span>
<span style="font-size: large;"><i><b><span style="color: #6fa8dc;">So, the answer is </span><span style="background-color: #6fa8dc;">24</span></b></i></span><br />
<span style="font-size: large;"><br /></span></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-12078884729360362382013-10-06T23:12:00.000-07:002013-10-06T23:12:45.310-07:00Riddle<div dir="ltr" style="text-align: left;" trbidi="on">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVcWLJP7He3I6J64xOFOAlO4Qe7klOF6Z9ieTeekQmqSgH8ocWWjNn_VysLdA_RvNgwMl_Soell6MAfCFOrd8SNPRo9z_ZVff6KHeUaekRlskjGWK50ugtqMl77wqiSMePdED0ti7kV6U/s1600/image001.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="297" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVcWLJP7He3I6J64xOFOAlO4Qe7klOF6Z9ieTeekQmqSgH8ocWWjNn_VysLdA_RvNgwMl_Soell6MAfCFOrd8SNPRo9z_ZVff6KHeUaekRlskjGWK50ugtqMl77wqiSMePdED0ti7kV6U/s640/image001.gif" width="640" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2dlq9J3xcscbZXzaV5qOjkCoRRPX7XRuYVO4sZRey066WSD2hbhsOdIG442xnjPVgxpxUR7uhiLi8XWYWhyrjgdvBmeK1ah3ExVFPOsqkq1SlPz4m562mO_CFkx0eiwpGNGT8qDOAAVI/s1600/image002.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="74" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2dlq9J3xcscbZXzaV5qOjkCoRRPX7XRuYVO4sZRey066WSD2hbhsOdIG442xnjPVgxpxUR7uhiLi8XWYWhyrjgdvBmeK1ah3ExVFPOsqkq1SlPz4m562mO_CFkx0eiwpGNGT8qDOAAVI/s640/image002.gif" width="640" /></a></div>
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjngqFpZTGNlPYx32h4vQeFMPiCjBW67fGXu98Ql0Z511ZcVuwLwSC7O2wlTITvPx47iiTgTlLJfTKfTOpNhyqQAx1mVxbZwHGeGhTwveNhiQFcTTA6pWgJh1wNSyNXUhiuFXmSaeTihdY/s1600/image003.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="90" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjngqFpZTGNlPYx32h4vQeFMPiCjBW67fGXu98Ql0Z511ZcVuwLwSC7O2wlTITvPx47iiTgTlLJfTKfTOpNhyqQAx1mVxbZwHGeGhTwveNhiQFcTTA6pWgJh1wNSyNXUhiuFXmSaeTihdY/s640/image003.gif" width="640" /></a></div>
<b><i><span style="font-size: large;">Wait for the answer..will be up tomorrow...</span></i></b></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-70112354917968539192013-10-04T22:26:00.003-07:002013-10-04T22:26:26.341-07:00NUMBER LINE FOR WHOLE NUMBERS<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal">
<b><i><span style="font-family: Cambria, serif; font-size: 16pt; line-height: 115%;"><span style="color: magenta;"><u>How to draw a number line?</u></span></span></i></b></div>
<div class="MsoNormal">
<span style="font-size: 7pt; text-indent: -0.25in;"><span style="color: #134f5c;"><b> </b></span></span></div>
<div class="MsoNormal">
<span style="font-size: 7pt; text-indent: -0.25in;"><span style="color: #134f5c;"><b><br />
</b></span></span></div>
<div class="MsoNormal">
<span style="color: #134f5c;"><b><span style="text-indent: -0.25in;"># </span><span style="font-size: 7pt; text-indent: -0.25in;"> </span><i style="text-indent: -0.25in;"><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">First draw a line</span></i></b></span></div>
<div class="MsoNormal">
<span style="color: #134f5c;"><b><br />
</b></span></div>
<div class="MsoNormal">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjp5k-tk60noP61bdxDD9AZFfKyKU4D6H0TVuRblCQbTqEWzNDzs2oW4LHlNk09KNGP8A3TsEcZJdYQpRZgkRu-oFVTUY6eMlXRklV56P0I4P9cl12vfFYw2XfMTRvjpYUIx4PMijpW-cI/s1600/line.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><span style="color: #134f5c;"><b><img border="0" height="14" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjp5k-tk60noP61bdxDD9AZFfKyKU4D6H0TVuRblCQbTqEWzNDzs2oW4LHlNk09KNGP8A3TsEcZJdYQpRZgkRu-oFVTUY6eMlXRklV56P0I4P9cl12vfFYw2XfMTRvjpYUIx4PMijpW-cI/s320/line.bmp" width="320" /></b></span></a></div>
<div class="MsoNormal">
<span style="color: #134f5c;"><b><br />
</b></span></div>
<div class="MsoNormal">
<span style="color: #134f5c;"><b># <span style="font-family: Symbol; font-size: 16pt; line-height: 115%; text-indent: -0.25in;"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><i style="text-indent: -0.25in;"><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Mark a point on it. Label this point as 0.</span></i></b></span></div>
<div class="MsoNormal">
<span style="color: #134f5c;"><b><br />
</b></span></div>
<div class="MsoNormal">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7aZ2Vt7HaRMZTE2wBeEE6N_UlWvps1vztplVyo75PCtfk4UQrt4ouP2cwEllgvw-9zL17QFffOIFPE-WG1xxHHIQKt1HbpNbfdBlhWHueKhb3KnKz809nYVWk4w2SkUGJ6GwJV3BrGfE/s1600/zero.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><span style="color: #134f5c;"><b><img border="0" height="46" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7aZ2Vt7HaRMZTE2wBeEE6N_UlWvps1vztplVyo75PCtfk4UQrt4ouP2cwEllgvw-9zL17QFffOIFPE-WG1xxHHIQKt1HbpNbfdBlhWHueKhb3KnKz809nYVWk4w2SkUGJ6GwJV3BrGfE/s320/zero.bmp" width="320" /></b></span></a></div>
<div class="MsoNormal">
<b><span style="color: #134f5c;"># </span><span style="color: #134f5c; font-size: 7pt; text-indent: -0.25in;"> </span><i style="text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 16pt; line-height: 115%;"><span style="color: #134f5c;">Mark a point on the right of this point and label it as 1. The distance between 0 and 1 is called </span><span style="color: magenta;"><u>unit distance.</u></span></span></i></b></div>
<div class="MsoNormal">
<span style="color: #134f5c;"><b><br />
</b></span></div>
<div class="MsoNormal">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6SsM5ggRdo1gQVjsntvaCjv4CJGXfxu25ageoaVOH-i4KrJr4KCp3FsL1klVP3dJ8pQF2GOvAe44Wq2fmSBQ2WD0EsQszRQKi25U1C7zDsimsjGQAfCTxQIwziVRYqIpbQ96bax6zz0A/s1600/1.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><span style="color: #134f5c;"><b><img border="0" height="46" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6SsM5ggRdo1gQVjsntvaCjv4CJGXfxu25ageoaVOH-i4KrJr4KCp3FsL1klVP3dJ8pQF2GOvAe44Wq2fmSBQ2WD0EsQszRQKi25U1C7zDsimsjGQAfCTxQIwziVRYqIpbQ96bax6zz0A/s320/1.bmp" width="320" /></b></span></a></div>
<div class="MsoNormal">
<span style="color: #134f5c;"><b><br />
</b></span></div>
<div class="MsoNormal">
<span style="color: #134f5c;"><b># <i><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: major-latin;">Mark another point to the right of 1 keeping the same distance as between 0 and 1 that is at unit distance. Label it as 2. </span></i></b></span></div>
<div class="MsoNormal">
<span style="color: #134f5c;"><b><br />
</b></span></div>
<div class="MsoNormal">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiOoGjq-DjFIitVk5MP79P7eF8-BcjWYlbOWZdSbVhkqKRkAp7_-LMiQMjB_1fA7po8nqFdjkzGo6vHGibttt4S6DA1DXzh1v5vMETaI1ZqJuQGvNMg0vLEO8_wByc-7nqN2cNw7e4rYk/s1600/2.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><span style="color: #134f5c;"><b><img border="0" height="46" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiOoGjq-DjFIitVk5MP79P7eF8-BcjWYlbOWZdSbVhkqKRkAp7_-LMiQMjB_1fA7po8nqFdjkzGo6vHGibttt4S6DA1DXzh1v5vMETaI1ZqJuQGvNMg0vLEO8_wByc-7nqN2cNw7e4rYk/s320/2.bmp" width="320" /></b></span></a></div>
<div class="MsoNormal">
<span style="color: #134f5c;"><b><br />
</b></span></div>
<div class="MsoNormal">
<span style="color: #134f5c;"><b># <span style="font-family: Symbol; font-size: 16pt; line-height: 115%; text-indent: -0.25in;"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><i style="text-indent: -0.25in;"><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">In this way we can label other points 3, 4, 5, 6 and so on in this manner.</span></i></b></span></div>
<div class="MsoNormal">
<span style="color: #134f5c;"><b><br />
</b></span></div>
<div class="MsoNormal">
<b><span style="color: #134f5c;"># </span><span style="color: #134f5c; font-family: Symbol; font-size: 16pt; line-height: 115%; text-indent: -0.25in;"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><i style="text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 16pt; line-height: 115%;"><span style="color: #134f5c;">This is called a </span><span style="color: magenta;"><u>number line of whole numbers</u></span></span></i></b></div>
<div class="MsoNormal">
<span style="color: #134f5c;"><b><br />
</b></span></div>
<div class="MsoNormal">
<span style="color: #134f5c; margin-left: 1em; margin-right: 1em; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMF4wm-6yLnd0Otb4guH5ou-kmBwb-j4EUD3FSGc8n339t4dPMbbvgcfCQlA9g0emCEIjagIUk-maneoBGS7RHEAlcE5nm5zfqsgZb3VnlIq8Gl3tD1Bd_GDDHT2QvCzP1EgCnQbXsVHc/s1600/number+line.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><b><img border="0" height="57" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMF4wm-6yLnd0Otb4guH5ou-kmBwb-j4EUD3FSGc8n339t4dPMbbvgcfCQlA9g0emCEIjagIUk-maneoBGS7RHEAlcE5nm5zfqsgZb3VnlIq8Gl3tD1Bd_GDDHT2QvCzP1EgCnQbXsVHc/s320/number+line.bmp" width="320" /></b></a></span></div>
<div class="MsoNormal">
<b><br />
</b></div>
<div class="MsoNormal">
<b><i><span style="font-family: Cambria, serif; font-size: 16pt; line-height: 115%;"><span style="color: magenta;"><u>Applications of number line</u></span></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: red; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><br />
</span></i></b></div>
<div class="MsoNormal">
<i><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><span style="color: #134f5c;"><b>Using a number line, we can:</b></span></span></i></div>
<div class="MsoNormal">
<i><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><span style="color: #134f5c;"><b><br />
</b></span></span></i></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
</div>
<ul style="text-align: left;">
<li><span style="color: #134f5c;"><b><span style="font-size: 16pt; line-height: 115%; text-indent: -0.25in;"><span style="font-family: Symbol;"> </span></span><span style="font-family: Cambria, serif; font-size: 16pt; font-style: italic; line-height: 115%; text-indent: -0.25in;">Compare two numbers(Find greater or smaller)</span></b></span></li>
<li><span style="color: #134f5c;"><b><span style="font-size: 16pt; line-height: 115%; text-indent: -0.25in;"><span style="font-family: Symbol;"> </span></span><span style="font-family: Cambria, serif; font-size: 16pt; font-style: italic; line-height: 115%; text-indent: -0.25in;">Add two whole numbers</span></b></span></li>
<li><i style="text-indent: -0.25in;"><span style="color: #134f5c;"><b><span style="font-size: 16pt; line-height: 115%;"><span style="font-family: Cambria, serif;"> </span></span><span style="font-family: Cambria, serif; font-size: 16pt; line-height: 115%;">Subtract two numbers</span></b></span></i></li>
</ul>
<br />
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoNormal">
</div>
<div class="MsoListParagraphCxSpLast">
<i><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><b>Next on the blog….Comparison of two numbers using number line…<o:p></o:p></b></span></i></div>
<div class="MsoNormal">
<i style="text-indent: -0.25in;"><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><b><span style="color: #134f5c;"><br />
</span></b></span></i></div>
<div class="MsoListParagraph" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<i><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><span style="color: #134f5c;"><b><o:p></o:p></b></span></span></i></div>
<div class="MsoListParagraph" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<i><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><span style="color: #134f5c;"><b><o:p></o:p></b></span></span></i></div>
<div class="MsoNormal">
<i><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: major-latin;"><span style="color: #134f5c;"><b><br />
</b></span></span></i></div>
<div class="MsoNormal">
<i style="text-indent: -0.25in;"><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><b><span style="color: #134f5c;"><br />
</span></b></span></i></div>
<div class="MsoNormal">
<i style="text-indent: -0.25in;"><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><span style="color: #134f5c;"><b><br />
</b></span></span></i></div>
<div class="MsoListParagraph" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<i><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><span style="color: #134f5c;"><b><o:p></o:p></b></span></span></i></div>
<div class="separator" style="clear: both; text-align: center;">
<span style="color: #134f5c;"><b><br />
</b></span></div>
<div class="separator" style="clear: both; text-align: center;">
<span style="color: #134f5c;"><b><br />
</b></span></div>
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<br /></div>
</div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-28664629338882037612013-10-02T22:50:00.001-07:002013-10-02T22:50:01.352-07:00TANGENT (A direction to success): WHOLE NUMBERS<a href="http://tangentmath.blogspot.com/2013/10/whole-numbers.html?spref=bl">TANGENT (A direction to success): WHOLE NUMBERS</a>: What are counting numbers? When we be...Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-31778888020104903052013-10-02T22:48:00.002-07:002013-10-02T22:48:37.547-07:00WHOLE NUMBERS<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal">
<b><i><u><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><span style="color: #cc0000;">What are
counting numbers?</span><o:p></o:p></span></u></i></b></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2rJ2JxyBv0wF5Xoxt0IEPpxvrAx3igd8tdxQygmy92xhe99Qqii_gcMLukI9CxUMh6Q39YKlSBzyJ4oRatwNa_vIbDLleOm_-NVN_6B5OicLvhehq850VsLGxSOfh7gFDEvq-FYvbJjs/s1600/numbers.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2rJ2JxyBv0wF5Xoxt0IEPpxvrAx3igd8tdxQygmy92xhe99Qqii_gcMLukI9CxUMh6Q39YKlSBzyJ4oRatwNa_vIbDLleOm_-NVN_6B5OicLvhehq850VsLGxSOfh7gFDEvq-FYvbJjs/s1600/numbers.bmp" /></a></div>
<div class="MsoNormal">
<b><i><u><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><span style="color: #cc0000;"><br /></span></span></u></i></b></div>
<div class="MsoNormal">
<span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><i>When
we begin to count, we begin with 1, 2, 3, 4…they come naturally. So, these
numbers are called Natural Numbers. </i></span><i style="font-family: Cambria, serif; font-size: 16pt; line-height: 115%;">Natural
numbers start from 1.</i></div>
<div class="MsoNormal">
<span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><i><br /></i></span></div>
<div class="MsoNormal">
<span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><i>From
all natural numbers, we chose a number say 7.<o:p></o:p></i></span></div>
<div class="MsoNormal">
<span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><i>We
know there is a number before 7 and a number after 7.<o:p></o:p></i></span></div>
<div class="MsoNormal">
<span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><i>If
we add 1 to 7 we get 7 + 1 = 8. ‘8’ is
called the successor of 7.<o:p></o:p></i></span></div>
<div class="MsoNormal">
<span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><i>If
we subtract 1 from 7 we get 7 – 1 = 6. ‘6’ is called the predecessor of 7.<o:p></o:p></i></span></div>
<div class="MsoNormal">
<span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><i><br /></i></span></div>
<div class="MsoNormal">
<span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><i><br /></i></span></div>
<div class="MsoNormal">
<i><b><u><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><span style="color: #cc0000;">Successor
and Predecessor</span></span></u></b><u><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><o:p></o:p></span></u></i></div>
<div class="MsoNormal">
<i><b><u><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><span style="color: #cc0000;"><br /></span></span></u></b></i></div>
<div class="MsoNormal">
<i><b><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><span style="color: #3d85c6;">Successor:</span></span></b><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"> The
successor of a number is the number obtained by adding 1 to it.<o:p></o:p></span></i></div>
<div class="MsoNormal">
<span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><i>1
is the successor of 0, 2 is the successor of 1, 2 is the successor of 1 and so
on…<o:p></o:p></i></span></div>
<div class="MsoNormal">
<span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><i><br /></i></span></div>
<div class="MsoNormal">
<i><b><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><span style="color: #3d85c6;">Predecessor</span>:</span></b><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"> The
Predecessor of a number is the number obtained by subtracting 1 from it.<o:p></o:p></span></i></div>
<div class="MsoNormal">
<i><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><br /></span></i></div>
<div class="MsoNormal">
<span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><i>1
is the Predecessor of 2, 2 is the Predecessor of 3 and so on.<o:p></o:p></i></span></div>
<div class="MsoNormal">
<span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><i>Note
that 1 does not have a Predecessor in natural numbers.<o:p></o:p></i></span></div>
<div class="MsoNormal">
<span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><i><br /></i></span></div>
<div class="MsoNormal">
<b><i><u><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><span style="color: #cc0000;">Whole
Numbers</span><o:p></o:p></span></u></i></b></div>
<div class="MsoNormal">
<b><i><u><span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><span style="color: #cc0000;"><br /></span></span></u></i></b></div>
<div class="MsoNormal">
<span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><i>If
we add 0 to the collection of Natural numbers we get whole numbers. All basic
operations such as addition, subtraction, multiplication and division can be
applied on Whole numbers.<o:p></o:p></i></span></div>
<div class="MsoNormal">
<span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><i>So,
1 has a predecessor in whole numbers that is 0 but 0 does not have a
predecessor.<o:p></o:p></i></span></div>
<div class="MsoNormal">
<span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><i><br /></i></span></div>
<br />
<div class="MsoNormal">
<span style="font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><i><b>Next
we will be discussing number line….</b></i><o:p></o:p></span></div>
</div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-80372145866249644662013-09-30T22:43:00.001-07:002013-09-30T22:43:00.824-07:00TANGENT (A direction to success): TANGENT (A direction to success): PLACE VALUE<a href="http://tangentmath.blogspot.com/2013/09/tangent-direction-to-success-place-value.html?spref=bl">TANGENT (A direction to success): TANGENT (A direction to success): PLACE VALUE</a>: TANGENT (A direction to success): PLACE VALUE : What will be the expansion of a two digit number like: 87 80 X 10 + 7 X 1 = 87 ( 7 is at...Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-58218944534084522322013-09-30T22:30:00.001-07:002013-09-30T22:40:40.376-07:00Its Time for Answers<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">A1.
</span></i></b><b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-latin;">23794206>23756819>5032790>5032786>987876<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-latin;"><br /></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-latin;">A2. 2500000<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<span style="font-family: Verdana, sans-serif; font-size: 10.5pt; line-height: 115%;"><br />
</span><b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">A3.
72600705 = (7 x1,00,00,000 )+(2 x 10,00,000)+(6 x 1,00,000) + (7 x 100) + (5 x
1)<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><br /></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">A4.
</span></i></b><b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-latin;">(i)1000 (ii)1 (iii) Whole (iv)4,01,108<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-latin;"><br /></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-latin;">A5.</span></i></b><span style="font-family: MathJax_Main, serif; font-size: 13.5pt; line-height: 115%;"> </span><b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-latin;">450,300</span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-latin;"><br />
</span></i></b><b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">A6.
</span></i></b><b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-latin;">$ 470,925, four hundred seventy thousand nine hundred and
twenty five dollars</span></i></b><b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-latin;"><br /></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">A7.186
Glasses<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><br /></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">A8.
</span></i></b><b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-latin;">Greatest number is 25286; smallest number is 25210<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-latin;"><br /></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-latin;">A9. 964320<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-latin;"><br /></span></i></b></div>
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-hansi-theme-font: major-latin;">A10. 600087<8014257 font=""></8014257></span></i></b><b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-hansi-theme-font: major-latin;"><!--8014257--><!--8014257--></span></i></b><br />
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-hansi-theme-font: major-latin;"><br /></span></i></b>
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-hansi-theme-font: major-latin;">Hope these help you</span></i></b><br />
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-hansi-theme-font: major-latin;">
<!--[if !supportLineBreakNewLine]--><br />
<!--[endif]--></span></i></b><br />
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-hansi-theme-font: major-latin;"><br /></span></i></b>
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-hansi-theme-font: major-latin;"><br /></span></i></b>
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-hansi-theme-font: major-latin;"><br /></span></i></b>
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-hansi-theme-font: major-latin;"><br /></span></i></b>
<div>
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-hansi-theme-font: major-latin;"><br /></span></i></b></div>
<div>
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-hansi-theme-font: major-latin;"><br /></span></i></b></div>
</div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-9568482445327022302013-09-30T04:20:00.001-07:002013-09-30T04:20:41.646-07:00TANGENT (A direction to success): PLACE VALUE<a href="http://tangentmath.blogspot.com/2013/09/place-value.html?spref=bl">TANGENT (A direction to success): PLACE VALUE</a>: What will be the expansion of a two digit number like: 87 80 X 10 + 7 X 1 = 87 ( 7 is at ones place and 8 at tens place) Similarly...Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-1373713576321425032013-09-29T23:14:00.000-07:002013-09-29T23:14:09.460-07:00PLACE VALUE<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #741b47;">What
will be the expansion of a two digit number like: </span><span style="color: #351c75;">87</span><span style="color: #741b47;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #351c75; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #6aa84f;">80
X 10 + 7 X 1 = 87 ( 7 is at ones place and 8 at tens place)</span><span style="color: #741b47;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #6aa84f;"><br /></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">Similarly
an expansion of a three digit number </span><span style="color: #351c75; font-family: Georgia, Times New Roman, serif;">427 </span><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">will be:<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #6aa84f;">4
X 100 + 2 X 10 + 7 X 1 = 427</span><span style="color: #741b47;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #6aa84f;"><br /></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">So,
here we can say that 7 is at ones place, 2 is at tens place and 4 is at
hundreds place.<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">If
this idea is extended to a four digit number say</span><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #351c75;"> 2138</span><span style="color: #741b47;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">It
can be written as:<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #6aa84f;">2
X 1000 + 1 x 100 + 3 x 10 + 8 X 1</span><span style="color: #741b47;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">Here,
8 is at ones place, 3 at tens place, 1 at hundreds place and 2 at thousands
place.<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">Further
extending to a 5-digit number say for example </span><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #351c75;">28373</span><span style="color: #741b47;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">It
can be written in the expanded form as:<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #38761d;">2
X 10000 + 8 X 1000 + 3 X 100 + 7 X 10 + 3 X 1</span><span style="color: #741b47;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">That
is 3 is at ones place, 7 at tens place, 3 at hundreds place, 8 at thousands
place, 2 at ten thousands place. <o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">When
we want to write this number in words, we write it as:<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #6aa84f;">Twenty
eight thousand three hundred and seventy three.</span><span style="color: #741b47;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><i><u><span style="font-size: 12pt; line-height: 115%;"><br /></span></u></i></span></b></div>
<div class="MsoNormal">
<b><span style="font-family: Georgia, Times New Roman, serif;"><i><u><span style="line-height: 115%;"><span style="color: magenta; font-size: large;">Now
let us introduce 1, 00, 000</span></span></u></i><i style="color: #741b47;"><span style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></i></span></b></div>
<div class="MsoNormal">
<b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><i><u><span style="line-height: 115%;"><span style="font-size: large;"><br /></span></span></u></i></span></b></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: red;">What
is the greatest 5-digit number?</span><span style="color: #741b47;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #351c75; font-family: Georgia, Times New Roman, serif;">99,999</span><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">
that is </span><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #6aa84f;">Ninety nine thousand nine hundred and ninety nine.</span><span style="color: #741b47;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #6aa84f;"><br /></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">If
we add 1 to the largest 5 digit number, what will we get?<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">We
get </span><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #6aa84f;">99,999 + 1 = 1,00, 000</span><span style="color: #741b47;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">Smallest
six digit number which is 1 Lakh<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">So,
now we may write any six digit number in words and can expand it.<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">Say,
</span><span style="color: #351c75; font-family: Georgia, Times New Roman, serif;">2, 34, 567</span><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"> in expanded form will be written as<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #6aa84f;">2
X 1,00,000 + 3 X10,000 + 4 X 1000 + 5 X 100 + 6 X 10 + 7 X 1</span><span style="color: #741b47;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #6aa84f;"><br /></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">Here
7 is at ones place, 6 at tens place, 4 at thousands place, 3 at ten thousands
place, and 2 at lakh place. <o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">In
words, it can be written as:<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #6aa84f;">Two
lakh, thirty four thousand, five hundred and sixty seven.</span><span style="color: #741b47;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">Further,<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif; font-size: 12pt;">If
we add 1 to the largest six digit number</span><span style="color: #351c75; font-family: Georgia, Times New Roman, serif; font-size: 12pt;"> 9,99,999</span><span style="color: #741b47; font-family: Georgia, Times New Roman, serif; font-size: 12pt;"> we get the smallest 7-digit
number that is </span><span style="color: #351c75; font-family: Georgia, Times New Roman, serif; font-size: 12pt;">10,00,000 </span><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><span style="font-size: small;">called </span><span style="font-size: large;">ten lakh.</span><span style="font-size: small;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><span style="font-size: large;"><br /></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif; font-size: 12pt;">If
we add 1 to the largest seven digit number </span><span style="color: #351c75; font-family: Georgia, Times New Roman, serif; font-size: 12pt;">99,99,999</span><span style="color: #741b47; font-family: Georgia, Times New Roman, serif; font-size: 12pt;"> we get the smallest 8-digit
number that is </span><span style="color: #351c75; font-family: Georgia, Times New Roman, serif; font-size: 12pt;">1,00,00,000</span><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><span style="font-size: small;"> called </span><span style="font-size: large;">one crore.</span><span style="font-size: small;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><span style="font-size: large;"><br /></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: magenta; font-size: large;">READING AND WRITING LARGE NUMBERS</span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: magenta; font-size: large;"><br /></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">So,
now for reading and writing large numbers <o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">We
make a table<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">For
example if we want to expand a three digit number </span><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #351c75;">347</span><span style="color: #741b47;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">We
write it in table form as<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: red;">H T O Expansion</span><span style="color: #741b47;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #6aa84f;">3 4 7 3 X 100 + 4 X 10 + 7 X 1</span><span style="color: #741b47;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #6aa84f;"><br /></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">Where
H stands for hundreds, T stands for tens and O stands for ones.<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">Similarly,
large numbers can be expanded by the same manner by putting the digits in a
tabular form called placement boxes.<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">Say
3, 54, 67, 243 can be written as<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<br /></div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableLightShadingAccent2" style="border-collapse: collapse; border: none; mso-border-bottom-alt: solid #C0504D 1.0pt; mso-border-bottom-themecolor: accent2; mso-border-top-alt: solid #C0504D 1.0pt; mso-border-top-themecolor: accent2; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184; width: 679px;">
<tbody>
<tr style="height: 14.45pt; mso-yfti-firstrow: yes; mso-yfti-irow: -1;">
<td style="border-bottom: solid #C0504D 1.0pt; border-left: none; border-right: none; border-top: solid #C0504D 1.0pt; height: 14.45pt; mso-border-bottom-themecolor: accent2; mso-border-top-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 77.4pt;" valign="top" width="103">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><i><span style="color: #943634; font-family: "Baskerville Old Face","serif"; font-size: 12.0pt; mso-themecolor: accent2; mso-themeshade: 191;">Number<o:p></o:p></span></i></b></div>
</td>
<td style="border-bottom: solid #C0504D 1.0pt; border-left: none; border-right: none; border-top: solid #C0504D 1.0pt; height: 14.45pt; mso-border-bottom-themecolor: accent2; mso-border-top-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 40.5pt;" valign="top" width="54">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><i><span style="color: #943634; font-family: "Baskerville Old Face","serif"; font-size: 12.0pt; mso-themecolor: accent2; mso-themeshade: 191;">T.Cr<o:p></o:p></span></i></b></div>
</td>
<td style="border-bottom: solid #C0504D 1.0pt; border-left: none; border-right: none; border-top: solid #C0504D 1.0pt; height: 14.45pt; mso-border-bottom-themecolor: accent2; mso-border-top-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 42.8pt;" valign="top" width="57">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><i><span style="color: #943634; font-family: "Baskerville Old Face","serif"; font-size: 12.0pt; mso-themecolor: accent2; mso-themeshade: 191;">Cr<o:p></o:p></span></i></b></div>
</td>
<td style="border-bottom: solid #C0504D 1.0pt; border-left: none; border-right: none; border-top: solid #C0504D 1.0pt; height: 14.45pt; mso-border-bottom-themecolor: accent2; mso-border-top-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 42.3pt;" valign="top" width="56">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><i><span style="color: #943634; font-family: "Baskerville Old Face","serif"; font-size: 12.0pt; mso-themecolor: accent2; mso-themeshade: 191;">T.lakh<o:p></o:p></span></i></b></div>
</td>
<td style="border-bottom: solid #C0504D 1.0pt; border-left: none; border-right: none; border-top: solid #C0504D 1.0pt; height: 14.45pt; mso-border-bottom-themecolor: accent2; mso-border-top-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 49.75pt;" valign="top" width="66">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><i><span style="color: #943634; font-family: "Baskerville Old Face","serif"; font-size: 12.0pt; mso-themecolor: accent2; mso-themeshade: 191;">Lakh<o:p></o:p></span></i></b></div>
</td>
<td style="border-bottom: solid #C0504D 1.0pt; border-left: none; border-right: none; border-top: solid #C0504D 1.0pt; height: 14.45pt; mso-border-bottom-themecolor: accent2; mso-border-top-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 49.85pt;" valign="top" width="66">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><i><span style="color: #943634; font-family: "Baskerville Old Face","serif"; font-size: 12.0pt; mso-themecolor: accent2; mso-themeshade: 191;">T.Th<o:p></o:p></span></i></b></div>
</td>
<td style="border-bottom: solid #C0504D 1.0pt; border-left: none; border-right: none; border-top: solid #C0504D 1.0pt; height: 14.45pt; mso-border-bottom-themecolor: accent2; mso-border-top-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 48.75pt;" valign="top" width="65">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><i><span style="color: #943634; font-family: "Baskerville Old Face","serif"; font-size: 12.0pt; mso-themecolor: accent2; mso-themeshade: 191;">Th<o:p></o:p></span></i></b></div>
</td>
<td style="border-bottom: solid #C0504D 1.0pt; border-left: none; border-right: none; border-top: solid #C0504D 1.0pt; height: 14.45pt; mso-border-bottom-themecolor: accent2; mso-border-top-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 55.15pt;" valign="top" width="74">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><i><span style="color: #943634; font-family: "Baskerville Old Face","serif"; font-size: 12.0pt; mso-themecolor: accent2; mso-themeshade: 191;">Hundred<o:p></o:p></span></i></b></div>
</td>
<td style="border-bottom: solid #C0504D 1.0pt; border-left: none; border-right: none; border-top: solid #C0504D 1.0pt; height: 14.45pt; mso-border-bottom-themecolor: accent2; mso-border-top-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 53.25pt;" valign="top" width="71">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><i><span style="color: #943634; font-family: "Baskerville Old Face","serif"; font-size: 12.0pt; mso-themecolor: accent2; mso-themeshade: 191;">Tens <o:p></o:p></span></i></b></div>
</td>
<td style="border-bottom: solid #C0504D 1.0pt; border-left: none; border-right: none; border-top: solid #C0504D 1.0pt; height: 14.45pt; mso-border-bottom-themecolor: accent2; mso-border-top-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 49.85pt;" valign="top" width="66">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><i><span style="color: #943634; font-family: "Baskerville Old Face","serif"; font-size: 12.0pt; mso-themecolor: accent2; mso-themeshade: 191;">Ones<o:p></o:p></span></i></b></div>
</td>
</tr>
<tr style="height: 29.75pt; mso-yfti-irow: 0; mso-yfti-lastrow: yes;">
<td style="background: #EFD3D2; border-bottom: solid #C0504D 1.0pt; border: none; height: 29.75pt; mso-background-themecolor: accent2; mso-background-themetint: 63; mso-border-bottom-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 77.4pt;" valign="top" width="103">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><i><span style="color: #943634; font-family: "Baskerville Old Face","serif"; font-size: 12.0pt; mso-themecolor: accent2; mso-themeshade: 191;">3, 54, 67, 243<o:p></o:p></span></i></b></div>
</td>
<td style="background: #EFD3D2; border-bottom: solid #C0504D 1.0pt; border: none; height: 29.75pt; mso-background-themecolor: accent2; mso-background-themetint: 63; mso-border-bottom-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 40.5pt;" valign="top" width="54">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
</td>
<td style="background: #EFD3D2; border-bottom: solid #C0504D 1.0pt; border: none; height: 29.75pt; mso-background-themecolor: accent2; mso-background-themetint: 63; mso-border-bottom-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 42.8pt;" valign="top" width="57">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<i><span style="color: #943634; font-family: "Baskerville Old Face","serif"; font-size: 12.0pt; mso-themecolor: accent2; mso-themeshade: 191;">3<o:p></o:p></span></i></div>
</td>
<td style="background: #EFD3D2; border-bottom: solid #C0504D 1.0pt; border: none; height: 29.75pt; mso-background-themecolor: accent2; mso-background-themetint: 63; mso-border-bottom-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 42.3pt;" valign="top" width="56">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<i><span style="color: #943634; font-family: "Baskerville Old Face","serif"; font-size: 12.0pt; mso-themecolor: accent2; mso-themeshade: 191;">5<o:p></o:p></span></i></div>
</td>
<td style="background: #EFD3D2; border-bottom: solid #C0504D 1.0pt; border: none; height: 29.75pt; mso-background-themecolor: accent2; mso-background-themetint: 63; mso-border-bottom-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 49.75pt;" valign="top" width="66">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<i><span style="color: #943634; font-family: "Baskerville Old Face","serif"; font-size: 12.0pt; mso-themecolor: accent2; mso-themeshade: 191;">4<o:p></o:p></span></i></div>
</td>
<td style="background: #EFD3D2; border-bottom: solid #C0504D 1.0pt; border: none; height: 29.75pt; mso-background-themecolor: accent2; mso-background-themetint: 63; mso-border-bottom-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 49.85pt;" valign="top" width="66">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<i><span style="color: #943634; font-family: "Baskerville Old Face","serif"; font-size: 12.0pt; mso-themecolor: accent2; mso-themeshade: 191;">6<o:p></o:p></span></i></div>
</td>
<td style="background: #EFD3D2; border-bottom: solid #C0504D 1.0pt; border: none; height: 29.75pt; mso-background-themecolor: accent2; mso-background-themetint: 63; mso-border-bottom-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 48.75pt;" valign="top" width="65">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<i><span style="color: #943634; font-family: "Baskerville Old Face","serif"; font-size: 12.0pt; mso-themecolor: accent2; mso-themeshade: 191;">7<o:p></o:p></span></i></div>
</td>
<td style="background: #EFD3D2; border-bottom: solid #C0504D 1.0pt; border: none; height: 29.75pt; mso-background-themecolor: accent2; mso-background-themetint: 63; mso-border-bottom-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 55.15pt;" valign="top" width="74">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<i><span style="color: #943634; font-family: "Baskerville Old Face","serif"; font-size: 12.0pt; mso-themecolor: accent2; mso-themeshade: 191;">2<o:p></o:p></span></i></div>
</td>
<td style="background: #EFD3D2; border-bottom: solid #C0504D 1.0pt; border: none; height: 29.75pt; mso-background-themecolor: accent2; mso-background-themetint: 63; mso-border-bottom-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 53.25pt;" valign="top" width="71">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<i><span style="color: #943634; font-family: "Baskerville Old Face","serif"; font-size: 12.0pt; mso-themecolor: accent2; mso-themeshade: 191;">4<o:p></o:p></span></i></div>
</td>
<td style="background: #EFD3D2; border-bottom: solid #C0504D 1.0pt; border: none; height: 29.75pt; mso-background-themecolor: accent2; mso-background-themetint: 63; mso-border-bottom-themecolor: accent2; padding: 0in 5.4pt 0in 5.4pt; width: 49.85pt;" valign="top" width="66">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<i><span style="color: #943634; font-family: "Baskerville Old Face","serif"; font-size: 12.0pt; mso-themecolor: accent2; mso-themeshade: 191;">3<o:p></o:p></span></i></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal">
<br /></div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184; width: 679px;"><tbody>
</tbody></table>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">This
number in expanded form will be:<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #6aa84f;">3
X 1,00,00,000 + 5 X 10,00,000 + 4 X 1,00,000 + 6 X 10,000 + 7 X 1000 + 2 X 100
+ 4 X 10 + 3 X 1</span><span style="color: #741b47;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #6aa84f;"><br /></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">And
in words:<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #6aa84f;">Three
crore, fifty four lakhs, sixty seven thousand two hundred and forty three.</span><span style="color: #741b47;"><o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #6aa84f;"><br /></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><span style="font-size: small;">In
the </span><span style="font-size: large;">Indian system of numeration </span><span style="font-size: small;">the commas between the digits are placed and
are used to mark thousands, lakhs and crores.<o:p></o:p></span></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">We
start by putting the first comma from the right after the thousands place that
is three digits from right, then after two digits later that is after five
digits from right, third comma after two digits again that is 7 digits from
right. This marks crore<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">So,
for the number above 35467243, the commas are put as 3, 54, 67, 243<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<br /></div>
<br />
<div class="MsoNormal">
<br /></div>
</div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-41657480206203924172013-09-26T02:45:00.001-07:002013-09-29T23:15:17.350-07:00TANGENT (A direction to success): Practice Questions(Knowing our Numbers)<div dir="ltr" style="text-align: left;" trbidi="on">
<a href="http://tangentmath.blogspot.com/2013/09/practice-questionsknowing-our-numbers.html?spref=bl">TANGENT (A direction to success): Practice Questions(Knowing our Numbers)</a>: Here are some questions based on this chapter... Specially for mothers and teachers... make your child solve these questions for practi...</div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-73451710195167549122013-09-26T02:39:00.001-07:002013-09-29T23:15:34.324-07:00Practice Questions(Knowing our Numbers)<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal">
<span style="color: red; font-family: Cambria, serif;"><span style="font-size: 21px; line-height: 24px;"><b><i>Here are some questions based on this chapter... </i></b></span></span></div>
<div class="MsoNormal">
<span style="color: red; font-family: Cambria, serif;"><span style="font-size: 21px; line-height: 24px;"><b><i>Specially for mothers and teachers... make your child solve these questions for practice...</i></b></span></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-family: Cambria, serif; font-size: 16pt; line-height: 115%;"><span style="color: magenta;">Qs1.</span></span><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">
Arrange the following in descending order:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">5032786,
23794206, 5032790, 23756819, 987876<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><br /></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="font-family: Cambria, serif; font-size: 16pt; line-height: 115%;"><span style="color: magenta;">Qs2.</span></span><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">
Determine the product of the two place values of the two fives in 750956.<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><br /></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="font-family: Cambria, serif; font-size: 16pt; line-height: 115%;"><span style="color: magenta;">Qs3.</span></span><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">
Replace each blank with a multiple of 10, 10 or 1:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">72600705
= (7 x …)+(2 x …)+(6 x …) + (7 x …) + (5 x …)<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><br /></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="font-family: Cambria, serif; font-size: 16pt; line-height: 115%;"><span style="color: magenta;">Qs4.</span></span><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">
Fill up:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">(i)….
Thousand make a million<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">(ii)
The smallest counting number is …<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">(iii)
0, 1, 2, 3, 4, 5 are set of … numbers<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">(iv)
Four hundred one thousand one hundred and eight<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><br /></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="font-family: Cambria, serif; font-size: 16pt; line-height: 115%;"><span style="color: magenta;">Qs5.</span></span><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">
Estimate the product:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">786
x 567<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><br /></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="font-family: Cambria, serif; font-size: 16pt; line-height: 115%;"><span style="color: magenta;">Qs6.</span></span><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">
The cost of an office table is Rs 1365. How much will 345 tables cost. Write your
answer in numbers?<o:p></o:p></span></i></b></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGgDABQiJmqzTnvM3gvVnyGE_CDEDa8AJHVH94XEgtINEioH_Q5U2Be4_ehpjnavcO5EgRfXlo3Fk_56-WFAfs-cpGyZgwmOK_rNLpILAywPslE8MSuSirK2h3rV3qYXWurSyDAyFSFLA/s1600/table.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGgDABQiJmqzTnvM3gvVnyGE_CDEDa8AJHVH94XEgtINEioH_Q5U2Be4_ehpjnavcO5EgRfXlo3Fk_56-WFAfs-cpGyZgwmOK_rNLpILAywPslE8MSuSirK2h3rV3qYXWurSyDAyFSFLA/s1600/table.bmp" /></a></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><br /></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin; mso-no-proof: yes;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600"
o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f"
stroked="f">
<v:stroke joinstyle="miter"/>
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0"/>
<v:f eqn="sum @0 1 0"/>
<v:f eqn="sum 0 0 @1"/>
<v:f eqn="prod @2 1 2"/>
<v:f eqn="prod @3 21600 pixelWidth"/>
<v:f eqn="prod @3 21600 pixelHeight"/>
<v:f eqn="sum @0 0 1"/>
<v:f eqn="prod @6 1 2"/>
<v:f eqn="prod @7 21600 pixelWidth"/>
<v:f eqn="sum @8 21600 0"/>
<v:f eqn="prod @7 21600 pixelHeight"/>
<v:f eqn="sum @10 21600 0"/>
</v:formulas>
<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
<o:lock v:ext="edit" aspectratio="t"/>
</v:shapetype><v:shape id="Picture_x0020_1" o:spid="_x0000_i1026" type="#_x0000_t75"
style='width:207.75pt;height:106.5pt;visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\DOCUME~1\MEHAKC~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.wmz"
o:title="MC910217544[1]"/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span></i></b><b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="font-family: Cambria, serif; font-size: 16pt; line-height: 115%;"><span style="color: magenta;">Qs7.</span></span><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">
A vessel has 4 liters and 650ml of apple juice. How many glasses of 25ml
capacity can be filled with juice?<o:p></o:p></span></i></b></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-g4-iKB74uuXzGVxFdziAfDrB8svXccjL2YDi748ZHb6TFQEmCWRaRTgIptv1xw2p1wg442lZh0JXYnVOm3DkMZOsbkMx5-6ifBHeKPq_buIDClbAFdRA4MAI0MFCHuoo_hVCLWGLF9g/s1600/juice.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-g4-iKB74uuXzGVxFdziAfDrB8svXccjL2YDi748ZHb6TFQEmCWRaRTgIptv1xw2p1wg442lZh0JXYnVOm3DkMZOsbkMx5-6ifBHeKPq_buIDClbAFdRA4MAI0MFCHuoo_hVCLWGLF9g/s1600/juice.bmp" /></a></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><br /></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin; mso-no-proof: yes;"><!--[if gte vml 1]><v:shape id="Picture_x0020_2" o:spid="_x0000_i1025"
type="#_x0000_t75" style='width:100.5pt;height:1in;visibility:visible;
mso-wrap-style:square'>
<v:imagedata src="file:///C:\DOCUME~1\MEHAKC~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image003.wmz"
o:title="MC900264358[1]"/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span></i></b><b><i><span style="color: #76923c; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin; mso-themecolor: accent3; mso-themeshade: 191;"><o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="font-family: Cambria, serif; font-size: 16pt; line-height: 115%;"><span style="color: magenta;">Qs8.</span></span><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">
Find the greatest and the smallest of the following:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">25286,
25245, 25270, 25210.<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><br /></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="font-family: Cambria, serif; font-size: 16pt; line-height: 115%;"><span style="color: magenta;">Qs9.</span></span><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">
Largest number formed by the digits 2, 4, 0, 3, 6, 9<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><br /></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="font-family: Cambria, serif; font-size: 16pt; line-height: 115%;"><span style="color: magenta;">Qs10.</span></span><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"> Arrange the following in ascending order:<o:p></o:p></span></i></b></div>
<br />
<div class="MsoNormal">
<b><i><span style="color: #002060; font-family: "Cambria","serif"; font-size: 16.0pt; line-height: 115%; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">600087,
8014257, 8015632, 10012458, 8014306</span></i></b></div>
</div>
Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-7941314105244772471.post-63301357089010638842013-09-24T22:58:00.001-07:002013-09-24T22:58:33.490-07:00TANGENT (A direction to success): TANGENT (A direction to success): KNOWING OUR NUMB...<a href="http://tangentmath.blogspot.com/2013/09/tangent-direction-to-success-knowing.html?spref=bl">TANGENT (A direction to success): TANGENT (A direction to success): KNOWING OUR NUMB...</a>: TANGENT (A direction to success): KNOWING OUR NUMBERS : This is a chapter from Class 6 Read on to understand the chapter........ KNOWI...Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-54932974434353024022013-09-24T22:54:00.002-07:002013-09-29T23:16:24.788-07:00KNOWING OUR NUMBERS(Contd......)<div dir="ltr" style="text-align: left;" trbidi="on">
<h3>
</h3>
<h4>
<b><i><span style="color: #7030a0; font-family: 'Baskerville Old Face', serif; line-height: 18px;"><span style="font-size: large;">How to form numbers from given digits?</span></span></i></b></h4>
<div class="MsoNormal">
</div>
<ul>
<li><i><span style="line-height: 18px;"><b><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;">To write the greatest number using these digits we place the given digits in ascending order unless there is a Zero.</span></b></span></i></li>
</ul>
<br />
<div class="MsoNormal">
<i><span style="line-height: 18px;"><b><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><br /></span></b></span></i></div>
<div class="MsoNormal">
</div>
<ul>
<li><i><span style="line-height: 18px;"><b><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;">To write the smallest number using these digits we place the given digits in descending order unless there is a Zero.</span></b></span></i></li>
</ul>
<br />
<div class="MsoNormal">
<i><span style="line-height: 18px;"><b><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><br /></span></b></span></i></div>
<div class="MsoNormal">
</div>
<ul>
<li><i><span style="line-height: 18px;"><b><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;">If there is Zero in the given digits then Zero does not come in the first place.</span></b></span></i></li>
</ul>
<br />
<div class="MsoNormal">
<i><span style="line-height: 18px;"><b><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><br /></span></b></span></i></div>
<div class="MsoNormal">
</div>
<ul>
<li><i><span style="line-height: 18px;"><b><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;">In case of greatest Zero will come in the last place and in case of smallest Zero will come in the second place and the rest of digits in ascending order.</span></b></span></i></li>
</ul>
<br />
<div class="MsoNormal">
<i><span style="line-height: 18px;"><b><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><br /></span></b></span></i></div>
<h3>
<i><span style="line-height: 21px;"><b><span style="color: #351c75; font-family: Georgia, Times New Roman, serif; font-size: x-small;">Consider any Example to understand this concept.....</span></b></span></i></h3>
<div class="MsoNormal">
<i><span style="line-height: 18px;"><b><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="line-height: 18px;"><b><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><span style="color: #cc0000;">Given digits are:</span> 2, 8, 7, 4<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="line-height: 18px;"><b><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="line-height: 18px;"><b><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><span style="color: red;">Greatest Number = 8742 & Smallest Number </span>= 2478<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="line-height: 18px;"><b><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="line-height: 18px;"><b><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><span style="color: red;">Given digits are:</span> 2, 0, 5, 8<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="line-height: 18px;"><b><span style="color: red; font-family: Georgia, Times New Roman, serif; font-size: x-small;"><br /></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="line-height: 18px;"><b><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><span style="color: red;">Greatest Number </span>= 8520<o:p></o:p></span></b></span></i></div>
<div class="MsoNormal">
<i><span style="line-height: 18px;"><b><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><br /></span></b></span></i></div>
<br />
<div class="MsoNormal">
<i><span style="line-height: 18px;"><b><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><span style="color: red;">Smallest Number</span> = 2058 (not 0258)</span></b></span></i></div>
</div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-14008698583923865882013-09-23T22:50:00.001-07:002013-09-29T23:16:13.050-07:00TANGENT (A direction to success): KNOWING OUR NUMBERS<div dir="ltr" style="text-align: left;" trbidi="on">
<a href="http://tangentmath.blogspot.com/2013/09/knowing-our-numbers.html?spref=bl">TANGENT (A direction to success): KNOWING OUR NUMBERS</a>: This is a chapter from Class 6 Read on to understand the chapter........ KNOWING OUR NUMBERS Class 6 BASIC UNDERSTANDING When...</div>
Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-7941314105244772471.post-7759417392766679482013-09-23T22:49:00.001-07:002013-09-23T22:49:24.055-07:00Attention Students!!!!!<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal">
<span style="color: #7030a0; font-family: Georgia, Times New Roman, serif;"><span style="line-height: 18px;"><b><i>For the next topic in this chapter.......Follow......the next post will up soon....</i></b></span></span></div>
<div class="MsoNormal">
<span style="color: #7030a0; font-family: Georgia, Times New Roman, serif;"><span style="line-height: 18px;"><b><i>Any Questions on this topic, feel free to ask through the blog.....</i></b></span></span></div>
<div class="MsoNormal">
<span style="color: #7030a0; font-family: Georgia, Times New Roman, serif;"><span style="line-height: 18px;"><b><i>Sample Questions are on the way.....</i></b></span></span></div>
<div class="MsoNormal">
<span style="color: #7030a0; font-family: Georgia, Times New Roman, serif;"><span style="line-height: 18px;"><b><i><br /></i></b></span></span></div>
</div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-86615324279322296642013-09-23T22:46:00.001-07:002013-09-29T23:16:47.029-07:00KNOWING OUR NUMBERS<div dir="ltr" style="text-align: left;" trbidi="on">
<b><i><span style="color: #cc0000; font-family: Georgia, Times New Roman, serif; font-size: large;">This is a chapter from Class 6</span></i></b><br />
<b><i><span style="color: #cc0000; font-family: Georgia, Times New Roman, serif; font-size: large;">Read on to understand the chapter........</span></i></b><br />
<span style="font-family: Georgia, Times New Roman, serif;"><br /></span>
<br />
<div align="center" class="MsoNormal" style="text-align: center;">
<u><span style="color: #00b0f0; font-size: 16pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></span></u></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<u><span style="color: #00b0f0; font-size: 16pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">KNOWING OUR NUMBERS<o:p></o:p></span></span></u></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<u><span style="color: #00b0f0; font-size: 16pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">Class 6<o:p></o:p></span></span></u></div>
<div class="MsoNormal">
<b><i><u><span style="background-color: lime; background-position: initial initial; background-repeat: initial initial; color: #c00000; font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></span></u></i></b></div>
<div class="MsoNormal">
<span style="font-family: Georgia, Times New Roman, serif;"><b><i><u><span style="background-color: lime; background-position: initial initial; background-repeat: initial initial; color: #c00000; font-size: 12pt; line-height: 115%;">BASIC UNDERSTANDING</span></u></i></b><span style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></span></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">When
we want to count or measure we use a mathematical object known as Numbers.<o:p></o:p></span></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">Numbers
are used over years and its definition is extended to further branches which
are zero, negative numbers, natural numbers, whole numbers, rational numbers,
irrational numbers.<o:p></o:p></span></span></i></div>
<div class="MsoNormal">
<b><i><u><span style="background-color: lime; background-position: initial initial; background-repeat: initial initial; color: #c00000; font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></span></u></i></b></div>
<div class="MsoNormal">
<span style="font-family: Georgia, Times New Roman, serif;"><b><i><u><span style="background-color: lime; background-position: initial initial; background-repeat: initial initial; color: #c00000; font-size: 12pt; line-height: 115%;">COMPARING NUMBERS</span></u></i></b><span style="color: #c00000; font-size: 12pt; line-height: 115%;"><o:p></o:p></span></span></div>
<div class="MsoNormal">
<span style="font-family: Georgia, Times New Roman, serif;"><b><i><span style="color: #7030a0; font-size: 12pt; line-height: 115%;">How to find the greatest and the smallest numbers?</span></i></b><b><i><span style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></i></b></span></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">When
we compare two numbers the number of digits of the number may be equal or
unequal<o:p></o:p></span></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">If
the digits of given two numbers are unequal, then the number with more digits
will be greater than number with less digits<o:p></o:p></span></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">Suppose
the number of digits in two given numbers is equal. Then how will you find the
greater or smaller of the two numbers?<o:p></o:p></span></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">
<o:p></o:p></span></span></i></div>
<div class="MsoNormal">
<v:shapetype coordsize="21600,21600" filled="f" id="_x0000_t32" o:oned="t" o:spt="32" path="m,l21600,21600e"><span style="font-family: Georgia, Times New Roman, serif;">
<v:path arrowok="t" fillok="f" o:connecttype="none">
<o:lock shapetype="t" v:ext="edit">
</o:lock></v:path></span></v:shapetype><v:shape id="_x0000_s1026" o:connectortype="straight" style="flip: y; height: 1.5pt; margin-left: 49.5pt; margin-top: 16.65pt; position: absolute; width: 329.25pt; z-index: 251659264;" type="#_x0000_t32"><v:shape id="_x0000_s1027" o:connectortype="straight" style="height: 18pt; margin-left: 49.5pt; margin-top: 18.15pt; position: absolute; width: 0; z-index: 251660288;" type="#_x0000_t32">
<v:stroke endarrow="block"><span style="font-family: Georgia, Times New Roman, serif;">
</span></v:stroke></v:shape><v:shape id="_x0000_s1028" o:connectortype="straight" style="height: 108.75pt; margin-left: 214.5pt; margin-top: 19.65pt; position: absolute; width: 0; z-index: 251661312;" type="#_x0000_t32">
<v:stroke endarrow="block"><span style="font-family: Georgia, Times New Roman, serif;">
</span></v:stroke></v:shape><v:shape id="_x0000_s1029" o:connectortype="straight" style="height: 18pt; margin-left: 378.75pt; margin-top: 18.9pt; position: absolute; width: 0; z-index: 251662336;" type="#_x0000_t32">
<v:stroke endarrow="block"><span style="font-family: Georgia, Times New Roman, serif;">
</span></v:stroke></v:shape><i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;"> </span></span></i></v:shape></div>
<div class="MsoNormal">
<br /></div>
<span style="font-family: Georgia, Times New Roman, serif;"><br clear="ALL" />
</span><br />
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">The
Number with maximum The Number with minimum <o:p></o:p></span></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">Number
of digits is the greatest number of digits is the smallest<o:p></o:p></span></span></i></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;"> All
numbers have equal number of digits<o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">For
eg: Consider two numbers 5724 and 3253, Number of digits in both the numbers =
4<o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">The
digits at thousands place of both the numbers is<o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">For
5724 its is 5<o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">For
3253 is 3<o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">Now
5 >3<o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<v:shape id="_x0000_s1030" o:connectortype="straight" style="height: 18pt; left: 0; margin-left: 218.25pt; margin-top: 18.5pt; position: absolute; text-align: left; width: 0; z-index: 251663360;" type="#_x0000_t32">
<v:stroke endarrow="block"><span style="font-family: Georgia, Times New Roman, serif;">
</span></v:stroke></v:shape><i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">So, 5724 > 3253<o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">If
the digit at the thousands place is the same and the number of digits is also
the same then?<o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">For
eg : Consider the Numbers 5724 and 5352<o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">Here
number of digits of both the numbers = 4<o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">Digits
at thousands place = 5<o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">Digit
at hundreds place for 5724 = 7 and <o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">For
5352 is 3<o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">So,
7 > 3<o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<v:shape id="_x0000_s1031" o:connectortype="straight" style="height: 18pt; left: 0; margin-left: 230.25pt; margin-top: 22.3pt; position: absolute; text-align: left; width: 0; z-index: 251664384;" type="#_x0000_t32">
<v:stroke endarrow="block"><span style="font-family: Georgia, Times New Roman, serif;">
</span></v:stroke></v:shape><i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">Implies 5724 >
5352<o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">If
now the digits at the hundreds place of two numbers is the same then?<o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">For
eg: Consider two numbers 7432 and 7453<o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">At
thousands place both have 7<o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">At
hundreds place both have 4 <o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">But
at tens place 7432 has 3 and <o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">7453
has 5<o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">So,
3 < 5<o:p></o:p></span></span></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<v:shape id="_x0000_s1032" o:connectortype="straight" style="height: 18pt; left: 0; margin-left: 230.25pt; margin-top: 18.65pt; position: absolute; text-align: left; width: 0; z-index: 251665408;" type="#_x0000_t32">
<v:stroke endarrow="block"><span style="font-family: Georgia, Times New Roman, serif;">
</span></v:stroke></v:shape><i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">Therefore 7432
< 7453<o:p></o:p></span></span></i></div>
<div align="right" class="MsoNormal" style="text-align: right;">
<br /></div>
<div class="MsoNormal">
<i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;"> And we can proceed further in a similar manner<o:p></o:p></span></span></i></div>
<div class="MsoNormal">
<b><i><span style="color: #7030a0; font-size: 12pt; line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></span></i></b></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="color: #7030a0; font-family: Georgia, Times New Roman, serif;"><span style="line-height: 18px;"><b><i>For the next topic in this chapter.......Follow......the next post will up soon....</i></b></span></span></div>
<div class="MsoNormal">
<span style="color: #7030a0; font-family: Georgia, Times New Roman, serif;"><span style="line-height: 18px;"><b><i>Any Questions on this topic, feel free to ask...</i></b></span></span></div>
<div class="MsoNormal">
<span style="color: #7030a0; font-family: Georgia, Times New Roman, serif;"><span style="line-height: 18px;"><b><i>Sample Questions are on the way.....</i></b></span></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<br />
<div class="MsoNormal">
<br /></div>
</div>
Unknownnoreply@blogger.com4tag:blogger.com,1999:blog-7941314105244772471.post-38592161729168442272013-09-22T22:28:00.000-07:002013-09-22T22:29:28.356-07:00Quote of the day<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLFXRKxX-tQepQDlt65AlF4EZAHJQ9TKBLjNODydqwyf_rIpDDBWu5ask-pG7g4LCK_cTQILj5LDdotbIxDkW-LBKjzJVrh7PjRTNo5e5z5EJU78VKxRqBJPLf13WYb77tkxkef2tQp-w/s1600/Quote.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="250" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLFXRKxX-tQepQDlt65AlF4EZAHJQ9TKBLjNODydqwyf_rIpDDBWu5ask-pG7g4LCK_cTQILj5LDdotbIxDkW-LBKjzJVrh7PjRTNo5e5z5EJU78VKxRqBJPLf13WYb77tkxkef2tQp-w/s400/Quote.bmp" width="400" /></a></div>
<br />
<br />
Lot more informative posts to come........keep following.....</div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-63585228029551240572013-09-22T08:07:00.001-07:002013-09-22T08:07:27.090-07:00TANGENT (A direction to success): Multiply upto 20X20 in your head<a href="http://tangentmath.blogspot.com/2013/09/multiply-upto-20x20-in-your-head.html?spref=bl">TANGENT (A direction to success): Multiply upto 20X20 in your head</a>: The Main thing that helps to be better in maths is to understand how it works. Can u Multiply upto 20X20 in your head Ill show you how...Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-67773390076967254722013-09-22T08:05:00.002-07:002013-09-22T08:05:57.639-07:00Multiply upto 20X20 in your head<div dir="ltr" style="text-align: left;" trbidi="on">
<h3 style="text-align: left;">
<span style="color: #741b47;">The Main thing that helps to be better in maths is to understand how it works.</span></h3>
<h3 style="text-align: left;">
<i><b><span style="color: #741b47;">Can u Multiply upto 20X20 in your head</span></b></i></h3>
<div>
<i><b><span style="color: #741b47;">Ill show you how.........</span></b></i></div>
<div>
<i><b><span style="color: #741b47;"><br /></span></b></i></div>
<div>
<i><b><span style="color: #741b47;">See for yourself with an example:</span></b></i></div>
<div>
<i><b><span style="color: #741b47;"><br /></span></b></i></div>
<div>
<i><b><span style="color: #741b47;">Take 17 X 15</span></b></i></div>
<div style="text-align: left;">
<ul style="text-align: left;">
<li><b><i><span style="color: #741b47;">Place the larger of the two on the top in your mind </span></i></b></li>
</ul>
</div>
<div style="text-align: left;">
<b><i><span style="color: #741b47;"><br /></span></i></b></div>
<div style="text-align: left;">
<span style="color: #741b47;"><b><i> </i></b><b><i><div class="separator" style="clear: both; display: inline !important; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikEa8tz1WqkAetdWTtA8sAIrg8XQTGmWt7inlVgt_ZNPwSPomNUCR9Vp-uH2mudqR-_Xt_c3ng5odqcEMUkGNvAYFPry9bmG-O590_7OYXZZRx15K0x2untxffe8UddqZQwAlS2U5AnnA/s1600/multiply.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikEa8tz1WqkAetdWTtA8sAIrg8XQTGmWt7inlVgt_ZNPwSPomNUCR9Vp-uH2mudqR-_Xt_c3ng5odqcEMUkGNvAYFPry9bmG-O590_7OYXZZRx15K0x2untxffe8UddqZQwAlS2U5AnnA/s1600/multiply.png" /></a></div>
</i></b></span></div>
<div style="text-align: left;">
<ul style="text-align: left;">
<li><span style="color: #741b47;"><b><i>Then draw a shape such that it covers 17 above and 5 from below </i></b><b><i><div class="separator" style="clear: both; display: inline !important; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdbfNZ8rGv3_f5BBn9-QEQU9AhMvaU8WvrSQfasOSn9xipq5__NQ_n1QhMGkKuJ8nRPEXe_FbGdZl8KNWTevtSlKMsOy7cpYQlwwgOAXX9Ux2LLGvaY2shvYn9bOD3oiKDEndhjPNmk0g/s1600/multiply.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdbfNZ8rGv3_f5BBn9-QEQU9AhMvaU8WvrSQfasOSn9xipq5__NQ_n1QhMGkKuJ8nRPEXe_FbGdZl8KNWTevtSlKMsOy7cpYQlwwgOAXX9Ux2LLGvaY2shvYn9bOD3oiKDEndhjPNmk0g/s1600/multiply.png" /></a></div>
</i></b></span></li>
</ul>
</div>
<div style="text-align: left;">
<b><i><span style="color: #741b47;">Those numbers are all you need.</span></i></b></div>
<div style="text-align: left;">
<ul style="text-align: left;">
<li><b><i><span style="color: #741b47;">Add 17 + 5 = 22</span></i></b></li>
<li><b><i><span style="color: #741b47;">Add zero behind it that is multiply it by 10 = 220</span></i></b></li>
<li><b><i><span style="color: #741b47;">Multiply the covered lower 5 and the single digit above it which is 7</span></i></b></li>
</ul>
<b><i><span style="color: #741b47;"> 7 X 5 = 35</span></i></b></div>
<div style="text-align: left;">
<ul style="text-align: left;">
<li><b><i><span style="color: #741b47;">Now add 220 + 35 = 225</span></i></b></li>
</ul>
<b><i><span style="color: #741b47;">ANY NUMBER UPTO 20 X 20 CAN BE MULTIPLIED MENTALLY BY THIS METHOD</span></i></b></div>
<div style="text-align: left;">
<b><i><span style="color: #741b47;">TRY IT FOR YOURSELF TAKING DIFFERENT NUMBERS. IT WILL MAKE YOUR CALCULATIONS EASY.</span></i></b></div>
<div style="text-align: left;">
<b><i><span style="color: #741b47;"><br /></span></i></b></div>
<div style="text-align: left;">
<b><i><br /></i></b></div>
</div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-43294183099228167922013-09-21T00:14:00.003-07:002013-09-21T00:14:30.664-07:00<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="color: #741b47; font-family: Georgia, Times New Roman, serif;"><b><i>Mathematics is a great motivator for all humans, because it starts with"zero" but it never ends"infinity"</i></b></span></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7941314105244772471.post-79172866466439293042013-09-21T00:05:00.002-07:002013-09-21T00:07:51.360-07:00Numbers are a journey from "Zero" to "Infinity"<div dir="ltr" style="text-align: left;" trbidi="on">
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<b><i><span style="font-size: 16.0pt; line-height: 115%;"><span style="color: #0b5394;">INFINITY:</span><span style="color: #741b47;"><o:p></o:p></span></span></i></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFO-NVWuRhKDNtg8pA0i8KitcpEhEJOc_ikCKH-JlwVCjDOjjvVXQeKKA4QThxaNRkBkxMSFvC8dGehM4kz09gmxkVnMasKBw3JGZRV7-7l_dr_v5_09TBTpCTwqDn3hPSBQEpztVNidA/s1600/infinity.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="color: #741b47;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFO-NVWuRhKDNtg8pA0i8KitcpEhEJOc_ikCKH-JlwVCjDOjjvVXQeKKA4QThxaNRkBkxMSFvC8dGehM4kz09gmxkVnMasKBw3JGZRV7-7l_dr_v5_09TBTpCTwqDn3hPSBQEpztVNidA/s1600/infinity.bmp" /></span></a><span style="color: #741b47;"><b><i><span style="font-size: 16.0pt; line-height: 115%; mso-no-proof: yes;"><!--[if gte vml 1]><v:shapetype
id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
<v:stroke joinstyle="miter"/>
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</v:shapetype><v:shape id="Picture_x0020_1" o:spid="_x0000_i1031" type="#_x0000_t75"
alt="http://images.wikia.com/halo/images/f/f9/Infinity.gif" style='width:84.75pt;
height:79.5pt;visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\DOCUME~1\MEHAKC~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.gif"
o:title="Infinity"/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span></i></b><b><i><span style="font-size: 16.0pt; line-height: 115%;">Infinity is an abstract concept that
describes anything without limit. One only has to imagine the sky to imagine
that space may go on forever.<o:p></o:p></span></i></b></span></div>
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<span style="color: #741b47;"><span style="font-size: 21px; line-height: 24px;"><b><i>Philosophically</i></b></span></span><b><i><span style="font-size: 16.0pt; line-height: 115%;"><span style="color: #741b47;"> there
are three different types of infinity<o:p></o:p></span></span></i></b></div>
<ul type="disc">
<li class="MsoNormal" style="background-color: white; background-position: initial initial; background-repeat: initial initial; text-align: justify;"><b><i><span style="font-size: 16.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><span style="color: #741b47;">Potential
or mathematical infinity: a process which has the potential of being
infinite. For example, counting the natural numbers 1, 2, 3, 4, 5, ... is
a potentially infinite task.<o:p></o:p></span></span></i></b></li>
<li class="MsoNormal" style="background-color: white; background-position: initial initial; background-repeat: initial initial; text-align: justify;"><b><i><span style="font-size: 16.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><span style="color: #741b47;">Actual
or physical infinity: an infinity which exists in nature. This category
includes the infinitely large and the infinitely small. Examples of
physical infinities would include the Universe (if it is infinite in
space) or Time (if it is infinite).<o:p></o:p></span></span></i></b></li>
<li class="MsoNormal" style="background-color: white; background-position: initial initial; background-repeat: initial initial; text-align: justify;"><b><i><span style="font-size: 16.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><span style="color: #741b47;">"Absolute"
infinity: God.<o:p></o:p></span></span></i></b></li>
</ul>
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<b><i><span style="font-size: 16.0pt; line-height: 115%;"><span style="color: #741b47;">We are going to talk
about the mathematical infinjity.<o:p></o:p></span></span></i></b></div>
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<b><i><span style="font-size: 16.0pt; line-height: 115%;"><span style="color: #741b47;">The word “infinity”
derived from the latin word “infinitas” that means unboundedness and Greek word
“ apeiros” meaning endless.<o:p></o:p></span></span></i></b></div>
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<b><i><span style="font-size: 16.0pt; line-height: 115%;"><span style="color: #741b47;">INFINITY is treated as
a number as it counts or measures things but it is not a number like all other
real numbers.<o:p></o:p></span></span></i></b></div>
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<b><i><u><span style="font-size: 16.0pt; line-height: 115%;"><span style="color: #0b5394;">HISTORY</span><span style="color: #741b47;"><o:p></o:p></span></span></u></i></b></div>
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<span style="color: #741b47;"><b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;">The<span class="apple-converted-space"> </span></span></i></b><b><i><span style="background: white; font-size: 16.0pt; line-height: 115%; mso-bidi-font-family: Arial;">ancient Indians<span class="apple-converted-space"> </span>and<span class="apple-converted-space"> </span></span>Greeks, unable to codify infinity in terms of a formalized
mathematical system, approached infinity as a philosophical concept.<o:p></o:p></i></b></span></div>
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<b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;"><span style="color: #741b47;">The symbol of infinity was used by the Romans
to express large quantities. It was “John Wallis” who was the first
mathematician to use the symbol to denote an infinite quantity.<o:p></o:p></span></span></i></b></div>
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<b><i><span style="font-size: 16pt;"><span style="color: #741b47;">In mathematics, the infinity symbol is used more often to
represent a potential infinity rather than to represent an actually
infinite quantity such as the ordinal numbers and cardinal numbers (which
use other notations). For instance, in the mathematical notation for summations
and limits such as </span></span></i></b></div>
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<b><i><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGpD64x40ZiW7TIEErq7kutvN74ufe8mtJogi0onWGZOkJbGHc-JUHMPpVqwVpb2S-E4PL-ceq1RrQQdR1ORGs2szuVMVjKFOytA8Cqyl7d8ZADyki_eaIDjbpvavTpK-q4EdqnaLbVko/s1600/exp.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: #741b47;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGpD64x40ZiW7TIEErq7kutvN74ufe8mtJogi0onWGZOkJbGHc-JUHMPpVqwVpb2S-E4PL-ceq1RrQQdR1ORGs2szuVMVjKFOytA8Cqyl7d8ZADyki_eaIDjbpvavTpK-q4EdqnaLbVko/s1600/exp.bmp" /></span></a></i></b></div>
<b><i><span style="color: #741b47;"><o:p></o:p></span></i></b><br />
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<span style="color: #741b47;"><b><i><span style="font-size: 16pt;"><!--[if gte vml 1]><v:shape id="Picture_x0020_4"
o:spid="_x0000_i1030" type="#_x0000_t75" alt=" \sum_{i=0}^{\infty} \frac{1}{2^i} = \lim_{x\to\infty}\frac{2^x-1}{2^{x-1}} = 2,"
style='width:157.5pt;height:35.25pt;visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\DOCUME~1\MEHAKC~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image003.gif"
o:title="frac{2^x-1}{2^{x-1}} = 2,"/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span></i></b><b><i><span style="font-size: 16pt;"><o:p></o:p></span></i></b></span></div>
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<b><i><span style="font-size: 16pt;"><span style="color: #741b47;">The infinity sign is conventionally interpreted as meaning
that the variable grows arbitrarily large (towards infinity) rather than
actually taking an infinite value.<o:p></o:p></span></span></i></b></div>
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<b><i><span style="font-size: 16pt;"><span style="color: #741b47;">In other areas than mathematics, the infinity symbol may take
on other related meanings; for instance, it has been used in book binding to
indicate that a book is printed on acid free paper and will therefore
be long-lasting.<o:p></o:p></span></span></i></b></div>
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<b><i><span style="font-size: 16pt;"><span style="color: #741b47;">In mathematics it is used in:<o:p></o:p></span></span></i></b></div>
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<b><i><u><span style="font-size: 16pt;"><span style="color: #0b5394;">Calculus</span><span style="color: #741b47;"><o:p></o:p></span></span></u></i></b></div>
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<span style="color: #741b47;"><span class="apple-converted-space"><b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;"> Lebinitz
</span></i></b></span><b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;">one of the
co-inventors of<span class="apple-converted-space"> </span></span></i></b><b><i><span style="font-size: 16.0pt; line-height: 115%;">infinitesimal calculus</span></i></b><b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;"> speculated widely about infinite numbers and their use in
mathematics. To Leibniz, both infinitesimals and infinite quantities were ideal
entities, not of the same nature as appreciable quantities, but enjoying the
same properties.</span><o:p></o:p></i></b></span></div>
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<b><i><u><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;"><span style="color: #0b5394;">Real Analysis</span><span style="color: #741b47;"><o:p></o:p></span></span></u></i></b></div>
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<span style="color: #741b47;"><b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;">In<span class="apple-converted-space"> </span></span></i></b><b><i><span style="background: white; font-size: 16.0pt; line-height: 115%; mso-bidi-font-family: Arial;">real analysis, the symbol <!--[if gte vml 1]><v:shape id="_x0000_i1029" type="#_x0000_t75"
alt="\infty" style='width:13.5pt;height:7.5pt;visibility:visible;
mso-wrap-style:square'>
<v:imagedata src="file:///C:\DOCUME~1\MEHAKC~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image004.gif"
o:title="infty"/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--><span class="apple-converted-space"> </span></span></i></b><b style="text-align: center;"><i><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRqfX3xgp3_FrBsOQdXNyaHOXRkNT7C3TxxTvGC5O25aqLlVVNJrvGHbfeFBrmtp6V2HgVhSW2Rx9pkjBCGxZF0DsjAjcuQhqTCWzWMh0uinQIPNLcgPOBrd62BRh5I-yTXSdmpntP8Y0/s1600/infin.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRqfX3xgp3_FrBsOQdXNyaHOXRkNT7C3TxxTvGC5O25aqLlVVNJrvGHbfeFBrmtp6V2HgVhSW2Rx9pkjBCGxZF0DsjAjcuQhqTCWzWMh0uinQIPNLcgPOBrd62BRh5I-yTXSdmpntP8Y0/s1600/infin.bmp" /></a></i></b><b><i>, called "infinity",
denotes an unbounded<span class="apple-converted-space"> </span>limit.</i></b></span></div>
<br />
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<b><i><u><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;"><span style="color: #0b5394;">Complex Analysis</span><span style="color: #741b47;"><o:p></o:p></span></span></u></i></b></div>
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<span style="color: #741b47;"><b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;">As in real analysis, in<span class="apple-converted-space"> </span></span></i></b><b><i><span style="background: white; font-size: 16.0pt; line-height: 115%; mso-bidi-font-family: Arial;">Complex anaysis<span class="apple-converted-space"> </span>the symbol</span></i></b></span></div>
<span style="color: #741b47;"></span><br />
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<span style="color: #741b47;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibu2K0WoPZDaTw3nQuXh5VKdP6mNxr9w5KnspJcWINPHLZMFDYSPXmQ7JmMLnBTqx_fTnlPmFdRYXOfmdsMvIbI-AaBm3qFK8J4GgRZO4fMnfC5NZAp26BITafNoxK1LS28seSxLgzgoY/s1600/infin.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibu2K0WoPZDaTw3nQuXh5VKdP6mNxr9w5KnspJcWINPHLZMFDYSPXmQ7JmMLnBTqx_fTnlPmFdRYXOfmdsMvIbI-AaBm3qFK8J4GgRZO4fMnfC5NZAp26BITafNoxK1LS28seSxLgzgoY/s1600/infin.bmp" /></a></span></div>
<span style="color: #741b47;">
<b><i><span style="background: white; font-size: 16.0pt; line-height: 115%; mso-bidi-font-family: Arial;"><span class="apple-converted-space"> </span></span></i></b><b><i><span style="font-size: 16.0pt; line-height: 115%; mso-no-proof: yes;"></span></i></b><b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;">, called "infinity", denotes an unsigned infinite<span class="apple-converted-space"> </span></span></i></b><b><i><span style="font-size: 16.0pt; line-height: 115%;">limit </span></i></b><span class="apple-converted-space"><b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;"> <div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizG65zvDlv0ba_XfMEBRB2SKg0BIv7SDvZCMHb3Hu8MwEEtYSEZunvbdFkkWvhJTBkz-dfwO7KB_V5wy1uMaOnRmGxHRADiRagMvun6oH3kTeaFmrGoQOFZcRbiUuR_LQ-d7ITlPqMckg/s1600/x+tends+to.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizG65zvDlv0ba_XfMEBRB2SKg0BIv7SDvZCMHb3Hu8MwEEtYSEZunvbdFkkWvhJTBkz-dfwO7KB_V5wy1uMaOnRmGxHRADiRagMvun6oH3kTeaFmrGoQOFZcRbiUuR_LQ-d7ITlPqMckg/s1600/x+tends+to.bmp" /></a></div>
</span></i></b></span><b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;">means that the magnitude</span></i></b><b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;"><div class="separator" style="clear: both; display: inline !important; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhC5uIZXuN_qvUY1UAbhvflnNMgA0XPV55JuiBQ_UFLujTM4Nb0FESMyafPsEsg2lSQkmcg1hanFWf1J0KcbFhKGjA_nxLh_N-LGctBDfogY9N1V3v8xBWnRlvvRULTwlU8msu0YPl82vg/s1600/absolute.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhC5uIZXuN_qvUY1UAbhvflnNMgA0XPV55JuiBQ_UFLujTM4Nb0FESMyafPsEsg2lSQkmcg1hanFWf1J0KcbFhKGjA_nxLh_N-LGctBDfogY9N1V3v8xBWnRlvvRULTwlU8msu0YPl82vg/s1600/absolute.bmp" /></a></div>
</span></i></b><b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;"></span></i></b><b><i><span style="font-size: 16.0pt; line-height: 115%; mso-no-proof: yes;"></span></i></b><span class="apple-converted-space"><b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;"> </span></i></b></span><b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;">of </span>x<span class="apple-converted-space"> grows
beyond any assigned value.</span></i></b></span><br />
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<b><i><u><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;"><span style="color: #0b5394;">Set theory</span><span style="color: #741b47;"><o:p></o:p></span></span></u></i></b></div>
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<span style="color: #741b47;"><b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;">A different form of “infinity” is the</span></i></b><b><i><span style="font-size: 16.0pt; line-height: 115%;"> ordinal</span></i></b><span class="apple-converted-space"><b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;"> </span></i></b></span><b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;">and<span class="apple-converted-space"> cardinal </span>infinities
of set theory.<span class="apple-converted-space"> </span></span></i></b><b><i><span style="font-size: 16.0pt; line-height: 115%;">Georg Cantor</span></i></b><span class="apple-converted-space"><b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;"> </span></i></b></span><b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;">developed a system of<span class="apple-converted-space">
transfinite numbers</span> in which the first transfinite cardinal is<span class="apple-converted-space"> </span></span></i></b><b><i><span style="font-size: 16.0pt; line-height: 115%;">aleph null</span></i></b><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjvj9Ky-YF9OVxGAfy8L_4Kyb4lpFYFvClxV2YhpmK7w598wUaq_2IP9-T-oNgQnBV6oWvj0jN0Dan3CJuF40kfJnfcvb4fSpBQ374ZFOapdRZWMRmjp9c_rkY8xSdIsziGcrTHKtbRrYU/s1600/null.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjvj9Ky-YF9OVxGAfy8L_4Kyb4lpFYFvClxV2YhpmK7w598wUaq_2IP9-T-oNgQnBV6oWvj0jN0Dan3CJuF40kfJnfcvb4fSpBQ374ZFOapdRZWMRmjp9c_rkY8xSdIsziGcrTHKtbRrYU/s1600/null.bmp" /></a><b><i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-size: 16pt; line-height: 115%;">, the cardinality of the set of<span class="apple-converted-space"> </span></span></i></b><b><i><span style="font-size: 16.0pt; line-height: 115%;">natural numbers.</span></i></b></span></div>
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<b><i><span style="font-size: 16.0pt; line-height: 115%;"><span style="color: #741b47;">Exploring the infinite
is a journey into paradox.</span><o:p></o:p></span></i></b></div>
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