A decimal representation of a non-negative real number r is its expression as a sequence of symbols consisting of decimal digits traditionally written with a single separator:

Commonly, ${\displaystyle b_{k}\neq 0}$ if ${\displaystyle k>1.}$ The sequence of the ${\displaystyle a_{i}}$—the digits after the dot—is generally infinite. If it is finite, the lacking digits are assumed to be 0. If all ${\displaystyle a_{i}}$ are 0, the separator is also omitted, resulting in a finite sequence of digits, which represents a natural number.

The decimal representation represents the infinite sum:

Every nonnegative real number has at least one such representation; it has two such representations (with ${\displaystyle b_{k}\neq 0}$ if ${\displaystyle k>0}$) if and only if one has a trailing infinite sequence of 0, and the other has a trailing infinite sequence of 9. For having a one-to-one correspondence between nonnegative real numbers and decimal representations, decimal representations with a trailing infinite sequence of 9 are sometimes excluded.