A repeating decimal, also called a recurring decimal, is a number whose decimal representation eventually becomes periodic (i.e., the same sequence of digits repeats indefinitely). The repeating portion of a decimal expansion is conventionally denoted with a vinculum so, for example,

The minimum number of digits that repeats in such a number is known as the decimal period.

Repeating decimal notation was implemented in versions of the Wolfram Language prior to 6 as `PeriodicForm`[`RealDigits`[*r*]]
after loading the add-on package `NumberTheory`ContinuedFractions``.

All rational numbers have either finite decimal expansions (i.e., are regular numbers; e.g., ) or repeating decimals (e.g., ). However, irrational numbers, such as neither terminate nor become periodic.

Numbers such as 0.5 are sometimes regarded as repeating decimals since .

The denominators of the first few unit fractions having repeating decimals are 3, 6, 7, 9, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, ... (OEIS A085837).

The repeating portion of a rational number can be found in the Wolfram Language using the command `RealDigits`[*r*][[1,-1]].
The number of digits in the repeating portion of the decimal expansion of a rational
number can also be found directly from the multiplicative
order of its denominator. The periods of the
decimal expansions of
for ,
2, ... are 0, 0, 1, 0, 0, 1, 6, 0, 1, 0, 2, 1, 6, 6, 1, 0, 16, 1, 18, ... (OEIS A051626), where 0 indicates that the number is
regular.

If is a repeating decimal and is a terminating decimal, them has a nonperiodic part whose length is that of and a repeating part whose length is that of (Wells 1986, p. 60).