In
Decimal Number System, We have studied the place value rule for whole numbers, as follows.

place value rule for Numbers :

The value of the right extreme place is one (1) or unity.

Value of the place increases as it moves to the left.

Value of the place becomes ten times, as we move one place to the left.

So

the value of the place second from right is ten times one and is equal to ten.

The value of the place third from right is ten times ten and is called hundred.

The value of the place, fourth from right is ten times hundred and is called thousand.

The place value chart of a four digit whole number with example is given below.

place value chart for four digit numbers :

Thousands' place

Hundreds' place

Tens' place

Units' place

4

9

3

6

In the above example, the value of 4936 = 4 thousands + 9 hundreds + 3 tens + 6 ones = 4,000 + 900 + 30 + 6 = 4936

Extension of Place value chart of whole numbers to Decimals

Based on the above discussion, we can say

If we start from a place and proceed to the RIGHT, the value of each place is 1⁄10th of the next place to the left.

Thus, 'hundreds place' is 1⁄10th of the 'thousands place', 'tens place' is 1⁄10th of the 'hundreds place', and the 'units place' is 1⁄10th of the 'tens place'.

What shall be the places to the right of the units place ?

The above discussion suggests that the first place to the right of units place should be 1⁄10th of a unit (1).

The second place to the right of units place must be 1⁄10 x 1⁄10 i.e.1⁄100th of a unit (1).

The third place to the right of units place must be 1⁄10 x 1⁄10 x 1⁄10 i.e.1⁄1000th of a unit (1)and so on.

This discussion gives us the Decimal place value chart for a decimal number which is given below with an example.

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Thus, by studying the above Decimal Place Value Chart we can observe that, in 2589.314, we have place value of 2 = 2 x 1000 = 2000 place value of 5 = 5 x 100 = 500 place value of 8 = 8 x 10 = 80 place value of 9 = 9 x 1 = 9 place value of 3 = 3 x 1⁄10 = 3⁄10 place value of 1 = 1 x 1⁄100 = 1⁄100 place value of 4 = 4 x 1⁄1000 = 4⁄1000

Hence, we can write 2589.314 in expanded form as 2000 + 500 + 80 + 9 + 3⁄10 + 1⁄100 + 4⁄1000 or 2000 + 500 + 80 + 9 + .3 + .01 + .004

Solve the following problems on Decimal Place Value Chart

Write the following decimals in figures.

Two Hundred Seventy Three Point Nine One Seven

Point Three two Four

Sixteen Point Eight Seven one

Write the place value of the digits one and two in the following Decimals.

982.145

615.002

3245.9871

Write each of the following decimals in expanded form.

3.76

789.123

46.72904

Write each of the following in short form.

700 + 60 + 8 + 1⁄10 + 3⁄100

9000 + 600 + 40 + 2 + 9⁄10 + 7⁄100 + 3⁄1000

4 + 2⁄10 + 1⁄1000 + 8⁄100000

For Answers see at the bottom of the page.

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