A
repeating or
recurring decimal is a way of representing
rational numbers in
base 10 arithmetic. The
decimal representation of a number is said to be repeating if it becomes
periodic (repeating its values at regular intervals) and the
infinitely-repeated portion is not
zero. For example, the decimal representation of ⅓ becomes periodic just after the
decimal point, repeating the single digit "3" for ever, i.e. 0.333…. A more complicated example is , whose decimal becomes periodic after the
second digit following the decimal point and then repeats the sequence "144" for ever, i.e. 5.8144144144…. At present, there is no single universally accepted notation or phrasing for repeating decimals.