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  + 5x10^{0  .}   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