Repeating decimal

Decimal representation of a number whose digits are periodic

A repeating decimal or recurring decimal is a decimal representation of a number whose digits are eventually periodic (that is, after some place, the same sequence of digits is repeated forever); if this sequence consists only of zeros (that is if there are only a finite number of nonzero digits), the decimal is said to be terminating, and is not considered as repeating. It can be shown that a number is rational if and only if its decimal representation is repeating or terminating. For example, the decimal representation of ⁠1/3⁠ becomes periodic just after the decimal point, repeating the single digit "3" forever, i.e.

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