**decimal**numeral system is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system.

^{}The way of denoting numbers in the decimal system is often referred to as

*Decimal notation*.

^{}

A

*decimal numeral*, or just

*decimal*, or, improperly

*decimal number*, refers generally to the notation of a number in the decimal system, which contains a decimal separator (for example 10.00 or 3.14159). Sometimes these terms are used for any numeral in the decimal system. A

*decimal*may also refer to any digit after the decimal separator, such as in "3.14 is the approximation of Ï€ to two decimals".

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 nonnegative 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. In this context, the usual decimals are sometimes called

*terminating decimals*. A repeating decimal, is an infinite decimal, that, after some place repeats indefinitely the same sequence of digits (for example 5.123144144144144... = 5.123144).

^{}An infinite decimal represents a rational number if and only if it is a repeating decimal or has a finite number of nonzero digits.