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 13 becomes periodic just after the decimal point, repeating the single digit "3" forever, i.e. 0.333.... A more complicated example is 3227555, 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 59353, which becomes periodic after the decimal point, repeating the 13-digit pattern "1886792452830" forever, i.e. 11.18867924528301886792452830....
Repeating Decimal Media
Relaciona os algarismos da dizima periodica com os algarismos utilizados na formação da fração geratriz
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