TANGENT (A direction to success): TANGENT (A direction to success): PLACE VALUE

TANGENT (A direction to success): TANGENT (A direction to success): PLACE VALUE: 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...

Its Time for Answers

A1. 23794206>23756819>5032790>5032786>987876

A2. 2500000

A3. 72600705 = (7 x1,00,00,000 )+(2 x 10,00,000)+(6 x 1,00,000) + (7 x 100) + (5 x 1)

A4. (i)1000 (ii)1 (iii) Whole (iv)4,01,108

A5. 450,300

A6. $ 470,925, four hundred seventy thousand nine hundred and twenty five dollars

A7.186 Glasses

A8. Greatest number is 25286; smallest number is 25210

A9. 964320

A10. 600087<8014257 font="">

Hope these help you

TANGENT (A direction to success): PLACE VALUE

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 ones place and 8 at tens place) Similarly...

PLACE VALUE

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 an expansion of a three digit number 427 will be:

4 X 100 + 2 X 10 + 7 X 1 = 427

So, here we can say that 7 is at ones place, 2 is at tens place and 4 is at hundreds place.

If this idea is extended to a four digit number say 2138

It can be written as:

2 X 1000 + 1 x 100 + 3 x 10 + 8 X 1

Here, 8 is at ones place, 3 at tens place, 1 at hundreds place and 2 at thousands place.

Further extending to a 5-digit number say for example 28373

It can be written in the expanded form as:

2 X 10000 + 8 X 1000 + 3 X 100 + 7 X 10 + 3 X 1

That is 3 is at ones place, 7 at tens place, 3 at hundreds place, 8 at thousands place, 2 at ten thousands place.

When we want to write this number in words, we write it as:

Twenty eight thousand three hundred and seventy three.

Now let us introduce 1, 00, 000

What is the greatest 5-digit number?

99,999 that is Ninety nine thousand nine hundred and ninety nine.

If we add 1 to the largest 5 digit number, what will we get?

We get 99,999 + 1 = 1,00, 000

Smallest six digit number which is 1 Lakh

So, now we may write any six digit number in words and can expand it.

Say, 2, 34, 567 in expanded form will be written as

2 X 1,00,000 + 3 X10,000 + 4 X 1000 + 5 X 100 + 6 X 10 + 7 X 1

Here 7 is at ones place, 6 at tens place, 4 at thousands place, 3 at ten thousands place, and 2 at lakh place.

In words, it can be written as:

Two lakh, thirty four thousand, five hundred and sixty seven.

Further,

If we add 1 to the largest six digit number 9,99,999 we get the smallest 7-digit number that is 10,00,000 called ten lakh.

If we add 1 to the largest seven digit number 99,99,999 we get the smallest 8-digit number that is 1,00,00,000 called one crore.

READING AND WRITING LARGE NUMBERS

So, now for reading and writing large numbers

We make a table

For example if we want to expand a three digit number 347

We write it in table form as

H   T  O                 Expansion

3   4   7                    3 X 100 + 4 X 10 + 7 X 1

Where H stands for hundreds, T stands for tens and O stands for ones.

Similarly, large numbers can be expanded by the same manner by putting the digits in a tabular form called placement boxes.

Say 3, 54, 67, 243 can be written as

Number	T.Cr	Cr	T.lakh	Lakh	T.Th	Th	Hundred	Tens	Ones
3, 54, 67, 243		3	5	4	6	7	2	4	3

This number in expanded form will be:

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

And in words:

Three crore, fifty four lakhs, sixty seven thousand two hundred and forty three.

In the Indian system of numeration the commas between the digits are placed and are used to mark thousands, lakhs and crores.

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

So, for the number above 35467243, the commas are put as 3, 54, 67, 243

TANGENT (A direction to success): Practice Questions(Knowing our Numbers)

TANGENT (A direction to success): Practice Questions(Knowing our Numbers): Here are some questions based on this chapter...  Specially for mothers and teachers... make your child solve these questions for practi...

Practice Questions(Knowing our Numbers)

Here are some questions based on this chapter... 

Specially for mothers and teachers... make your child solve these questions for practice...

Qs1. Arrange the following in descending order:

5032786, 23794206, 5032790, 23756819, 987876

Qs2. Determine the product of the two place values of the two fives in 750956.

Qs3. Replace each blank with a multiple of 10, 10 or 1:

72600705 = (7 x …)+(2 x …)+(6 x …) + (7 x …) + (5 x …)

Qs4. Fill up:

(i)…. Thousand make a million

(ii) The smallest counting number is …

(iii) 0, 1, 2, 3, 4, 5 are set of … numbers

(iv) Four hundred one thousand one hundred and eight

Qs5. Estimate the product:

786 x 567

Qs6. The cost of an office table is Rs 1365. How much will 345 tables cost. Write your answer in numbers?

Qs7. A vessel has 4 liters and 650ml of apple juice. How many glasses of 25ml capacity can be filled with juice?

Qs8. Find the greatest and the smallest of the following:

25286,  25245,  25270,  25210.

Qs9. Largest number formed by the digits 2, 4, 0, 3, 6, 9

Qs10.  Arrange the following in ascending order:

600087, 8014257, 8015632, 10012458, 8014306

TANGENT (A direction to success): TANGENT (A direction to success): KNOWING OUR NUMB...

TANGENT (A direction to success): TANGENT (A direction to success): KNOWING OUR NUMB...: TANGENT (A direction to success): KNOWING OUR NUMBERS : This is a chapter from Class 6 Read on to understand the chapter........ KNOWI...

KNOWING OUR NUMBERS(Contd......)

How to form numbers from given digits?

• To write the greatest number using these digits we place the given digits in ascending order unless there is a Zero.

• To write the smallest number using these digits we place the given digits in descending order unless there is a Zero.

• If there is Zero in the given digits then Zero does not come in the first place.

• 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.

Consider any Example to understand this concept.....

Given digits are: 2, 8, 7, 4

Greatest Number = 8742 & Smallest Number = 2478

Given digits are: 2, 0, 5, 8

Greatest Number = 8520

Smallest Number = 2058 (not 0258)

TANGENT (A direction to success): KNOWING OUR NUMBERS

TANGENT (A direction to success): KNOWING OUR NUMBERS: This is a chapter from Class 6 Read on to understand the chapter........ KNOWING OUR NUMBERS Class 6 BASIC UNDERSTANDING When...

Attention Students!!!!!

For the next topic in this chapter.......Follow......the next post will up soon....

Any Questions on this topic, feel free to ask through the blog.....

Sample Questions are on the way.....

KNOWING OUR NUMBERS

This is a chapter from Class 6
Read on to understand the chapter........

KNOWING OUR NUMBERS

Class 6

BASIC UNDERSTANDING

When we want to count or measure we use a mathematical object known as Numbers.

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.

COMPARING NUMBERS

How to find the greatest and the smallest numbers?

When we compare two numbers the number of digits of the number may be equal or unequal

If the digits of given two numbers are unequal, then the number with more digits will be greater than number with less digits

Suppose the number of digits in two given numbers is equal. Then how will you find the greater or smaller of the two numbers?

                                                             

 

The Number with maximum                                                       The Number with minimum

Number of digits is the greatest                                                   number of digits is the smallest

                                        All numbers have equal number of digits

For eg: Consider two numbers 5724 and 3253, Number of digits in both the numbers = 4

The digits at thousands place of both the numbers is

For 5724 its is 5

For 3253 is 3

Now 5 >3

So, 5724 > 3253

If the digit at the thousands place is the same and the number of digits is also the same then?

For eg : Consider the Numbers 5724 and 5352

Here number of digits of both the numbers = 4

Digits at thousands place = 5

Digit at hundreds place for 5724 = 7 and

For 5352 is 3

So, 7 > 3

Implies 5724 > 5352

If now the digits at the hundreds place of two numbers is the same then?

For eg: Consider two numbers 7432 and 7453

At thousands place both have 7

At hundreds place both have 4

But at tens place 7432 has 3 and

7453 has 5

So, 3 < 5

Therefore 7432 < 7453

                                      And we can proceed further in a similar manner

For the next topic in this chapter.......Follow......the next post will up soon....

Any Questions on this topic, feel free to ask...

Sample Questions are on the way.....

Quote of the day

Lot more informative posts to come........keep following.....

TANGENT (A direction to success): Multiply upto 20X20 in your head

TANGENT (A direction to success): Multiply upto 20X20 in your head: 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...

Multiply upto 20X20 in your head

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.........

See for yourself with an example:

Take 17 X 15

• Place the larger of the two on the top in your mind 

                                   

• Then draw a shape such that it covers 17 above and 5 from below            
  

Those numbers are all you need.

• Add 17 + 5 = 22
• Add zero behind it that is multiply it by 10  = 220
• Multiply the covered lower 5 and the single digit above it which is 7

   7 X 5 = 35

• Now add  220 + 35 = 225

ANY NUMBER UPTO 20 X 20 CAN BE MULTIPLIED MENTALLY BY THIS METHOD

TRY IT FOR YOURSELF TAKING DIFFERENT NUMBERS. IT WILL MAKE YOUR CALCULATIONS EASY.

Mathematics is a great motivator for all humans, because it starts with"zero" but it never ends"infinity"

Numbers are a journey from "Zero" to "Infinity"

INFINITY:

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.

Philosophically there are three different types of infinity

• 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.
• 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).
• "Absolute" infinity: God.

We are going to talk about the mathematical infinjity.

The word “infinity” derived from the latin word “infinitas” that means unboundedness and Greek word “ apeiros” meaning endless.

INFINITY is treated as a number as it counts or measures things but it is not a number like all other real numbers.

HISTORY

The ancient Indians and Greeks, unable to codify infinity in terms of a formalized mathematical system, approached infinity as a philosophical concept.

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.

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 

The infinity sign is conventionally interpreted as meaning that the variable grows arbitrarily large (towards infinity) rather than actually taking an infinite value.

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.

In mathematics it is used in:

Calculus

 Lebinitz one of the co-inventors of infinitesimal calculus 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.

Real Analysis

In real analysis, the symbol  , called "infinity", denotes an unbounded limit.

Complex Analysis

As in real analysis, in Complex anaysis the symbol

 , called "infinity", denotes an unsigned infinite limit  

means that the magnitude

 of x grows beyond any assigned value.

Set theory

A different form of “infinity” is the ordinal and cardinal  infinities of set theory. Georg Cantor developed a system of transfinite numbers in which the first transfinite cardinal is aleph null, the cardinality of the set of natural numbers.

Exploring the infinite is a journey into paradox.