Decimal Number System
The Decimal Number System uses base 10 and it includes the digits from 0 through 9. Don’t get confused, it is the common number system that we use in our daily life to calculate the things. The powers weighted values for each position will be as follows:
(Base 10)Number |
104 |
103 |
102 |
101 |
100 |
10-1 |
10-2 |
10-3 |
Value |
10000 |
1000 |
100 |
10 |
1 |
.1 |
.01 |
.001 |
In this way if I have a decimal number 218 and I want to represent it in above manner the number 218 will be represented in the following manner:
2 * 102 + 1 * 101 + 8 * 100
= 2 * 100 + 1 * 10 + 8 * 1
= 200 + 10 + 8
= 218
Now let us take an example of any fractional decimal number. Let we have a number 821.128. Each digit appearing to the left of the decimal point represents a value between zero and nine and the power of ten is represented by its position in the number (starting from 0).
Digits appearing to the right of the decimal point represent a value between zero and nine times an increasing negative power of ten. Let us see how:
8 * 102 + 2 * 101 + 1 * 100 + 1 * 10-1 + 2 * 10-2 + 8 * 10-3
= 8 * 100 + 2 * 10 + 1 * 1 + 1 * 0.1 + 2 * 0.01 + 8 * 0.001
= 800 + 20 + 1 + 0.1 + 0.02 + 0.008
= 821.128
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