What is the name for a repeating decimal?

The name for a repeating decimal is a recurring decimal. It is a decimal representation in which a digit or block of digits repeats indefinitely, such as 0.333... or 0.142857142857....

“Repeating decimal” and “recurring decimal” are standard synonyms. The repeating block is called the repetend; in 1/7, for example, the repetend is 142857. A bar placed over the repeating digits is another common notation: 0.\overline{3} represents 0.333... forever.

Recurring decimals arise naturally when fractions are converted using long division. If a remainder repeats, the same sequence of quotient digits must recur. In base ten, a fraction in lowest terms terminates only when its denominator has no prime factors other than 2 and 5; denominators with other prime factors produce recurring decimals.

A recurring decimal is not the same as a terminating decimal, which ends after a finite number of digits. It is also not an irrational decimal: rational numbers have decimal expansions that either terminate or repeat, while irrational numbers continue without terminating or repeating.