# Decimal

## Number in base-10 numeral system / From Wikipedia, the free encyclopedia

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The **decimal** numeral system (also called the **base-ten** positional numeral system and **denary** /ˈdiːnəri/[1] or **decanary**) 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.[2] The way of denoting numbers in the decimal system is often referred to as *decimal notation*.[3]

A *decimal numeral* (also often just *decimal* or, less correctly, *decimal number*), refers generally to the notation of a number in the decimal numeral system. Decimals may sometimes be identified by a decimal separator (usually "." or "," as in 25.9703 or 3,1415).[4] *Decimal* may also refer specifically to the digits after the decimal separator, such as in "3.14 is the approximation of π to *two decimals*". Zero-digits after a decimal separator serve the purpose of signifying the precision of a value.

The numbers that may be represented in the decimal system are the decimal fractions. That is, 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 (see decimal representation). In this context, the decimal numerals with a finite number of non-zero digits after the decimal separator are sometimes called *terminating decimals*. A *repeating decimal* is an infinite decimal that, after some place, repeats indefinitely the same sequence of digits (e.g., 5.123144144144144... = 5.123144).[5] An infinite decimal represents a rational number, the quotient of two integers, if and only if it is a repeating decimal or has a finite number of non-zero digits.