# Decimal number fraction

In this we will learn how to represent a decimal number with the fractional part. For this we take the following example :

Example 1: (75.65)10

Step 1: First we take the weights and put it in the format specified in the decimal number system done below

101    100                   10-1    10-2         ← Weights
 .
↑
Decimal point

Since the example above contains fractional part we must include the radix point or the decimal point.

Step 2: Values are assigned to the corresponding weights before and after the decimal point as shown below:

101    100                  10-1      10-2         ← Weights
 7 5 . 6 5
↑
Decimal point

Step 3: Now calculate the product of the values and associated weights as shown

7x101
5x100
.
6x10-1
5x10-2

Step 4: Sum the products obtained in step 3 accordingly on the either side of the decimal point as illustrated below

7x101  + 5x100  .   6x10-1  + 5x10-2

=  7x10  + 5x1  .   6x(1/10)  + 5x(1/100)

=  70  + 5  .   (6/10)  + (5/100)

=   75  .   0.6  + 0.05

=  (75  .  0.65)10

Some more examples that you can try

1. (154.97) 10
2. (1.1) 10
3. (0.984) 10
4. (800.007) 10