# DECIMAL PLACE VALUE CHART - SHORT AND EXPANDED FORMS OF DECIMALS, EXAMPLE, EXERCISE

### Revisiting of Place value chart of whole numbers

Decimals before Decimal Place Value Chart

if you have not already done so.

That knowledge is a prerequisite here.

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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### Decimal Place Value Chart

 Thousands 1000 Hundreds 100 Tens 10 Ones 1 Decimal Point Tenths 1⁄10 (0.1) Hundredths 1⁄100 (0.01) Thousandths 1⁄1000 (0.001) 2 5 8 9 . 3 1 4

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

2589.314 is called the ordinary or standard form.

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### Exercise on Decimal Place Value Chart

Solve the following problems on
Decimal Place Value Chart

1. Write the following decimals in figures.
1. Two Hundred Seventy Three Point Nine One Seven
2. Point Three two Four
3. Sixteen Point Eight Seven one
2. Write the place value of the digits
one and two in the following Decimals.
1. 982.145
2. 615.002
3. 3245.9871
3. Write each of the following decimals in expanded form.
1. 3.76
2. 789.123
3. 46.72904
4. Write each of the following in short form.
1. 700 + 60 + 8 + 1⁄10 + 3⁄100
2. 9000 + 600 + 40 + 2 + 9⁄10 + 7⁄100 + 3⁄1000
3. 4 + 2⁄10 + 1⁄1000 + 8⁄100000
For Answers see at the bottom of the page.

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### Answers to Exercise on Decimal Place Value Chart

1.
1. 273.917
2. .324
3. 16.871
2.
1. 2 ones, 1 tenths
2. 1 Hundreds, 2 thousandths
3. 2 thousands, 1 ten thousandths
3.
1. 3 + 7⁄10 + 6⁄100
2. 700 + 80 + 9 + 1⁄10 + 2⁄100 + 3⁄1000
3. 40 + 6 + 7⁄10 + 9⁄1000 + 4⁄100000
4.
1. 768.13
2. 9642.973
3. 4.20108