Q. Can you give some Overview of Decimal Number System?
The Decimal Number System uses base 10 and It includes the digits from 0 through 9. The weighted values for each position are as follows:
|
10^4
|
10^3
|
10^2
|
10^1
|
10^0
|
10^-1
|
10^-2
|
10^-3
|
|
10000
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1000
|
100
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10
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1
|
.1
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.01
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.001
|
In reality, though, the number 123 represents:
1 * 10^2 + 2 * 10^1 + 3 * 10^0 =
1 * 100 + 2 * 10 + 3 * 1 =
100 + 20 + 3 =
123
Every digit appearing to the left of the decimal point represents a value between zero and nine times power of ten represented by its position in the number. The Digits appearing to the right of the decimal point represent a value between zero and nine times an increasing negative power of ten. For illustration, the value 725.194 is represented as follows:
7 * 10^2 + 2 * 10^1 + 5 * 10^0 + 1 * 10^-1 + 9 * 10^-2 + 4 * 10^-3 =
7 * 100 + 2 * 10 + 5 * 1 + 1 * 0.1 + 9 * 0.01 + 4 * 0.001 =
700 + 20 + 5 + 0.1 + 0.09 + 0.004 =725.194
The base-10 (or decimal) system is the one which we commonly use and it uses combinations of 10 numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to represent every other number.
When the counting in base-10 we go through the sequence
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
At this point we have used all the numbers available to us and the counting proceeds by adding a second column to the left of the first, and returning the first column to 0. The Counting then continues by increasing the right hand column again until we again reach 9 at which point we increase the left hand column and again return the right hand one to zero.
10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20......
Following this process permits us to represent every number using the numbers 0-9 inclusive.
The Various columns in a number represent the different powers of 10 that go to making up that number. Therefore
5738 = (5 x 103) + (7 x 102) + (3 x 101) + (8 x 100)
The columns starting from the right are sometimes referred to as units, tens, hundreds, thousands etc.