We know that the numbers are formed using the 10 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. As we are using base 10 system, we use these 10 digits. If we are using base two system, we use the digits 0, 1 and in base 3 system, we use the digits 0, 1, 2 etc.. Under base 10 system, the numbers are expressed as rational or irrational form.

The rational numbers can be integers or decimals. The numbers written to the left of the decimal point are called integral parts and those written to the right of decimal point are called decimal parts. In this section let us discuss with the places of these digits using place value chart.

## Place Value Definition

What is a place value? It is the value of the place where the digit in a number is placed.For example: In 325 we have the digits 3, 2 and 5.
We read this number as "Three hundred and Twenty Five"
Because, five is in units ( one's ) place.
Two is in ten's place and
Three is in hundred's place

Therefore place value of FIVE is " 1 "
Place value of TWO is " 10 "
Place value of "THREE" is 100

Let us discuss with Place Value Charts before discussing more examples.

## Place Value Charts and Decimal Place Value

In the above chart we can see that the decimal column separates the digits into integer and decimal parts.
The digits written to the left of decimal are called integer parts or integral parts and the digits written to the right of the decimal are called decimal parts.

We can see the number 1 5 6 3 7 . 0 4 2 in the above table.
The number formed by the digits 1, 5, 6, 3, 7 which is 15,637 is called the integer or integral part of the number since it is to the left of the decimal point.

From the above table we can observe that 7 is in "ONES" place
3 is in "TENS" place
6 is in "HUNDREDS" place
5 is in "THOUSANDS" place
and 1 is in "TEN THOUSANDS" place

To the right of the decimal point we can see the digits 0, 4 and 2.
The digits 0, 4 and 2 form the decimal part of the number.
From the table we can observe that
0 is in "TENTHS" place
4 is in "HUNDREDTHS" place
2 is in "THOUSANDTHS" place

Therefore, to identify the place value of any digit in a number, we need to identify the place it occupies in the above "Place Value Chart".

In the above table we can see the places of digits to the right of the decimal point.
For the number, 34.50791, we can identify the place values as follows.
Place value of 4 is ONE
Place value of 3 is TENS
Place value of 5 is TENTHS
Place value of 0 is HUNDREDTHS
Place value of 7 is THOUSANDTHS
Place value of 9 is TEN THOUSANDTHS
Place value of 1 is HUNDRED THOUSANDTHS

## Place Value Number Line

To express the number 2.6 on the number line, we divide the space between 2 and 3 into 10 equal parts and locate the 6th division as the number 2.6, which is shown in the following number line.

Let us expand the divisions between 2 and 3 to locate 2.63.

Since 2.63 is greater than 2.6, let us divide the interval between 2.6 and 2.7 into 10 equal parts, the 3rd division will be location of 2.63 which is shown in the following figure.

Let us expand the division between 2.6 and 2.7 to locate 2.637.
Since 2.637 is greater than 2.63, let us divide the interval between 2.63 and 2.64 into 10 equal parts, the 7th division will be the location of 2.637 which is shown in the following figure.

## Place Value Examples

### Solved Examples

Question 1: Find the sum and difference of place values of 2 and 5 in the following number.
26754.
Solution:

We have 26,754
Place Value of 5 is 10
Place Value of 2 is 10,000
Sum of the above place values = 10 + 10,000 = 10,010
Difference of Place Values = 10,000 - 10 = 9990

Question 2: Find the sum of the place values of the 3's in the following number: 2435.013.
Solution:

We have 2,435.013
Place Value of 3 in the integer part is 10

Place value of 3 in the decimal part is $\frac{1}{1000}$

Sum of the two place values = 10 + $\frac{1}{1000}$ = 10.001

Question 3: Write the numbers in the standard form.

(a).   1 x 102  + 4 x 10 + 3 x 10-1 + 5 x 10-2 + 7 x 10-3

(b).   6 x 104 + 3 x 102 + 7 x  10-2 + 9 x 10-4

Solution:

(a)    We have, 1 x 102  + 4 x 10 + 3 x 10-1 + 5 x 10-2  + 7 x 10-3

= 100 + 40 + $\frac{3}{10}$ + $\frac{5}{100}$ + $\frac{7}{1000}$

= 140.357

(b) We have 6 x 104 + 3 x 102 + 7 x  10-2 + 9 x 10-4

= 60,000 + 300 + $\frac{7}{100}$ + $\frac{9}{1000}$

= 60,300.079.