## ::Decimal

### ::concepts

Decimal::numerals    Number::system    Decimal::which    Numbers::title    Notation::language    Systems::chinese

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The world's earliest decimal multiplication table was made from bamboo slips, dating from 305 BC, during the Warring States period in China.

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This article aims to be an accessible introduction. For the mathematical definition, see Decimal representation.

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The decimal numeral system (also called base 10 or occasionally denary) has ten as its base. It is the numerical base most widely used by modern civilizations.<ref>The History of Arithmetic, Louis Charles Karpinski, 200pp, Rand McNally & Company, 1925.</ref><ref>Histoire universelle des chiffres, Georges Ifrah, Robert Laffont, 1994 (Also: The Universal History of Numbers: From prehistory to the invention of the computer, Georges Ifrah, ISBN 0-471-39340-1, John Wiley and Sons Inc., New York, 2000. Translated from the French by David Bellos, E.F. Harding, Sophie Wood and Ian Monk)</ref>

Decimal notation often refers to a base 10 positional notation such as the Hindu-Arabic numeral system or rod calculus;<ref>Lam Lay Yong & Ang Tian Se (2004) Fleeting Footsteps. Tracing the Conception of Arithmetic and Algebra in Ancient China, Revised Edition, World Scientific, Singapore.</ref> however, it can also be used more generally to refer to non-positional systems such as Roman or Chinese numerals which are also based on powers of ten.

A decimal number, or just decimal, refers to any number written in decimal notation, although it is more commonly used to refer to numbers that have a fractional part separated from the integer part with a decimal separator (e.g. 11.25).

A decimal may be a terminating decimal, which has a finite fractional part (e.g. 15.600); a repeating decimal, which has an infinite (non-terminating) fractional part made up of a repeating sequence of digits (e.g. 5.8144); or an infinite decimal, which has a fractional part that neither terminates nor has an infinitely repeating pattern (e.g. 3.14159265...). Decimal fractions have terminating decimal representations and other fractions have decimal representations with repeating patterns, whereas irrational numbers have infinite decimal representations.

Decimal sections