# 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/10n, 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 ....103,102,101,100,10-1,10-2 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 102 +9 x 101 + 9 x 100

Here 102 is weight associated with digit in 100th place, 101 is the weight associated with digit in 10s place and 100 weight associated with digit in units place.