This article is about decimal expansion of real numbers. For finite decimal representation, see Decimal.
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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:
Here . is the decimal separator, k is a nonnegative integer, and are digits, which are symbols representing integers in the range 0, ..., 9.
Commonly, if The sequence of the —the digits after the dot—is generally infinite. If it is finite, the lacking digits are assumed to be 0. If all 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 if ) 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.[1]
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