Decimal Number System

The decimal number system is a radix-10 number system and therefore has 10 different symbols. These are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. All higher numbers after ‘9’ are represented in terms
of these 10 digits only. The process of writing higher-order numbers after ‘9’ consists in writing the second digit (i.e. ‘1’) first, followed by the other digits, one by one, to obtain the next 10 numbers
from ‘10’ to ‘19’. The next 10 numbers from ‘20’ to ‘29’ are obtained by writing the third digit (i.e. ‘2’) first, followed by digits ‘0’ to ‘9’, one by one. The process continues until we have exhausted all possible two-digit combinations and reached ‘99’. Then three-digit combinations begins. The  first three-digit number consists of the lowest two-digit number followed by ‘0’ (i.e. 100), and the
process continues.

The magnitude of a given decimal number can be expressed as the sum of the various digits multiplied by their weights.
As an illustration, in the case of the decimal number 1234.567, the integer part (i.e. 1234) can be expressed as
1234 = 4×10^0 +3×10^1+2×10^2 +1×10^3 = 4+30+200+1000 = 1234
and the fractional part can be expressed as
567 = 5×10^−1+6×10^−2 +7×10^−3 = 0.5+0.06+0.007 = 0.567

In  decimal number system 9’s and 10’s complements are used. The 9’s complement of a given decimal number is obtained by subtracting each digit from 9. For example, the 9’s complement of (1234)10 would be (8765)10. The 10’s complement is obtained by adding ‘1’ to the 9’s complement. The 10’s complement of (1234)10 is (8766)10.

 

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