Decimal Place Value

Basics of Decimals:

We know that when we divide any number by another number then the quotient may be whole number or in the decimal form. That numbers are the decimal numbers.

Simply we define that, the numbers which are written in decimal form or which includes the decimal point in them i.e. they are not the whole numbers these type of numbers are called as decimal numbers or decimals only.

For example:

  • 24, 56.789, 88.990, 2.4 etc all these numbers includes decimal points in them and are the decimal numbers. And these numbers are not the whole numbers.
  • But, the numbers like 2, 4, 56, 567, 8900 etc all are the whole numbers.
  • So main difference between decimal number and whole number is decimal numbers includes decimal point and whole numbers not include decimal point.

Also, the decimal number consist of two parts, one is the whole number part and other is the decimal part.

If we have taken the decimal number as 56.450, in this number the part which is left to the decimal point is called as whole number part. Here, 56 is the whole number part.

And the part which is right to the decimal point is called as decimal part. Here, 0.450 is the decimal part.

Similarly, if we have taken the number as 980.0067, in this number the decimal part is 0.0067 and the whole number part is 980.

Decimal place value:

We already know that, the place values for whole number which are ones, tens, hundreds, thousands and so on.

For example we take a whole number as 3456, in this number 6 is at ones place, 5 is at tens place, 4 is at hundreds place and 3 is at thousands place. Hence, we write their place values as follows:

In the whole number here 3456,

  • Place value of 6 = 6*1= 6
  • Place value of 5 = 5*10 = 50
  • Place value of 4= 4*100 = 400
  • Place value of 3 = 3*1000= 3000

Similarly, we can write the place values for decimal numbers also. To understand it see the following table.

The following table shows the place value chart for decimal numbers.

To understand in detail, we take an example of decimal number and from which we find place values of all the digits in it.

1) Consider the decimal number as 8947.321

  • Here, 89427 is the whole number part and 0.321 is the decimal part.
  • The place value chart for the number 8947.321 is as given below.
  • By checking the places of digits we write as follows.

For whole number part:

  • The place value of 7= 7
  • Place value of 4= 4*10 = 40
  • Place value of 9= 9*100 = 900
  • Place value of 8= 8*1000= 8000

Now, for decimal part:

  • Place value of 3 = 3/10 = 0.3
  • Place value of 2 = 2/100 = 0.02
  • Place value of 1 = 1/1000 = 0.001

Thus, in expanded form the number 8947.321 is written as

8947.321 = 8000 + 900 + 40 + 7 + 0.3 + 0.02 + 0.001

2) Consider the decimal number as 9981.542

  • Here, 9981is the whole number part and 0.542 is the decimal part.
  • The place value chart for the number 9981.542 is as given below.
  • By checking the places of digits we write as follows.

For whole number part:

  • The place value of 1= 1
  • Place value of 8= 8*10 = 80
  • Place value of 9= 9*100 = 900
  • Place value of 9= 9*1000= 9000

Now, for decimal part:

  • Place value of 5 = 5/10 = 0.5
  • Place value of 4 = 4/100 = 0.04
  • Place value of 2 = 2/1000 = 0.002

Thus, in expanded form the number 9981.542 is written as

9981.542 = 9000 + 900 + 80 + 1 + 0.5 + 0.04 + 0.002


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