Repeating decimal
Repeating decimal (or recurring decimal) is a decimal where the number or pattern repeats forever. Repeating decimal is resulted when dividing a number by a number that is not divisible except for certain cases like dividing any number by 5. For example, dividing 7 by 3 would result in a repeating decimal, which is 2.333... or 2.3. The number or group of numbers that repeats is called a repetend or reptend and the number of numbers in the repetend is called the period length. For 2.3, 3 is the repetend and the period length is 1.
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. 0.333.... A more complicated example is 3227/555, whose decimal becomes periodic at the second digit following the decimal point and then repeats the sequence "144" forever, i.e. 5.8144144144.... Another example of this is 593/53, which becomes periodic after the decimal point, repeating the 13-digit pattern "1886792452830" forever, i.e. 11.18867924528301886792452830....
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