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