En matemáticas, la representación decimal es una manera de escribir números reales positivos, por medio de potencias del número 10 (negativas y/o positivas). En el caso de los números naturales, la representación decimal corresponde a la escritura en base 10 usual; para los números racionales, se obtiene una representación decimal limitada, o ilimitada periódica si son números periódicos; si son irracionales, la representación decimal es ilimitada y no periódica.

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A decimal representation of a non-negative real number r is an expression in the form of a series, traditionally written as a sum where a0 is a nonnegative integer, and a1, a2, ... are integers satisfying 0 ≤ ai ≤ 9, called the digits of the decimal representation. The sequence of digits specified may be finite, in which case any further digits ai are assumed to be 0. Some authors forbid decimal representations with a trailing infinite sequence of "9"s.This restriction still allows a decimal representation for each non-negative real number, but additionally makes such a representation unique.The number defined by a decimal representation is often written more briefly as That is to say, a0 is the integer part of r, not necessarily between 0 and 9, and a1, a2, a3, ... are the digits forming the fractional part of r. Both notations above are, by definition, the following limit of a sequence: .

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