          # Decimal

The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary) 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 casually decimal number, refers generally to the notation of a number in the decimal numeral system. Decimals may sometimes be identified for containing a decimal separator (for example the "." in 10.00 or 3.14159). "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".

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 (see Decimal representation). In this context, the decimal numerals with a finite number of non–zero places 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 (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.

## Origin

Many numeral systems of ancient civilisations use ten and its powers for representing numbers, possibly because there are ten fingers on two hands and people started counting by using their fingers. Examples are Brahmi numerals, Greek numerals, Hebrew numerals, Roman numerals, and Chinese numerals. Very large numbers were difficult to represent in these old numeral systems, and only the best mathematicians were able to multiply or divide large numbers. These difficulties were completely solved with the introduction of the Hindu–Arabic numeral system for representing integers. This system has been extended to represent some non-integer numbers, called decimal fractions or decimal numbers for forming the decimal numeral system.

Other Languages
العربية: نظام عد عشري
azərbaycanca: Onluq sistemi
Bân-lâm-gú: Si̍p-chìn-hoat
беларуская (тарашкевіца)‎: Дзесятковая сыстэма зьлічэньня
chiShona: Muravanegumi
Cymraeg: Degol
Deutsch: Dezimalsystem
فارسی: ده‌دهی
한국어: 십진법
Bahasa Indonesia: Sistem bilangan desimal
isiXhosa: I-decimal
íslenska: Tugakerfi
Kreyòl ayisyen: Sistèm desimal
Lingua Franca Nova: Sistem desimal
Bahasa Melayu: Perpuluhan

norsk nynorsk: Titalssystemet
ਪੰਜਾਬੀ: ਇਸ਼ਾਰੀਆ
română: Sistem zecimal
Sesotho sa Leboa: Letlase la lesome
Simple English: Decimal
српски / srpski: Декадни систем
srpskohrvatski / српскохрватски: Dekadni sistem
தமிழ்: பதின்மம்
Tiếng Việt: Hệ thập phân

ייִדיש: דעצימאל  