# Decimal Number System

## What is Decimal Number System?

The decimal number system is familiar to all of us. We all use it in our day to day life in calculations and different aspects. A decimal number system is also called as base-10 number system whereas binary number is a base-2 system; there are only two digits 0 and 1 which for a binary number.A

*decimal number*contains a decimal separator (for example 11.00 or 3.1421).

The numbers that may be represented in the decimal system are the decimal fractions, that is the fractions of the form

*a*/10

^{n}, where

*a*is an integer, and

*n*is a non-negative integer.

The decimal system has been extended to

*infinite decimals*, for representing any real number, by using an infinite sequence of digits after the decimal separator.

There are 10 digits in the decimal number system, i.e., 0-9. All decimal numbers are combinations of these 10 digits. A decimal number system is weighted number system. This means that it has a positional weight and positional value associated with it. The weights that may be associated with decimal numbers are ....10

^{3},10

^{2},10

^{1},10

^{0},10

^{-1},10

^{-2}and so on. Every decimal number can be expressed as sum of products of weight associated with each digit and the digit itself.

**For Example**, 999=900 + 90 + 9

=9 x 10

^{2}+9 x 10

^{1}+ 9 x 10

^{0}

Here 10

^{2}is weight associated with digit in 100

^{th}place, 10

^{1}is the weight associated with digit in 10s place and 10

^{0}weight associated with digit in units place.