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Decimal Calculation

So far we have seen the calculations involving natural numbers only. Let’s work now with decimals.

Converting decimal system numbers to any other system

Suppose (12.725) is a number in decimal system which is required to be converted into octal system (8 digits)

We will first convert 12 into octal system.
(12)10 = (14)8

Now to convert (0.725)10 into ( )8, we will apply the following method:
 
0.725 × 8 = 5.8 Take out integral part from here.
0.8 × 8 = 6.4 Take out integral part from here.
0.4 × 8 = 3.2 Take out integral part from here.
0.2 × 8 = 1.6 Take out integral part from here.
 
And keep doing this till we get decimal part as zero, i.e., the product should be an integer.
 
(0.725)10 = (0.5632…)8
 
So, (12.725) = (14.5632…)8

Converting any other system numbers to decimal system

Now suppose if (15.453)7 is to be converted into decimal system, then the process is as follows:
 
We will first convert (15)7 into decimal system.
(15)7 = 1 × 71 + 5 × 70 = (12)10
Now (0.453)7 = 4 × 7-1 + 5 × 7-2 + 3 × 7-3 = 0.6821
So, (15.453)7 = (12.6821)10





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