# Decimal

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

#### Dear Wikiwand AI, let's keep it short by simply answering these key questions:

Can you list the top facts and stats about Decimal?

Summarize this article for a 10 year old

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 (*decimal fractions*) of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as *decimal notation*.^{[2]}

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).^{[3]}
*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. Decimal fractions also result from the addition of an integer and a *fractional part*; the resulting sum sometimes is called a *fractional number*.

Decimals are commonly used to approximate real numbers. By increasing the number of digits after the decimal separator, one can make the approximation errors as small as one wants, when one has a method for computing the new digits.

Originally and in most uses, a decimal has only a finite number of digits after the decimal seperator. However, 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 usual decimals, 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).^{[4]} 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.