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Periodic Fraction

A periodic fraction is equivalent to a Series in which the terms are fractions and the pattern of the terms repeats.

If we exclude the case where the period is a non-zero fraction, a periodic fraction expresses a rational number that is not a decimal number.

Example

The fraction $\dfrac{2}{27}$ is a periodic fraction because: $\dfrac{2}{27}=\dfrac{74}{1000}+\dfrac{74}{1\ 000\ 000}+ \ldots$ which we can also write as: $\dfrac{2}{27}=0.074074074\ldots=0.\overline {074}$ .

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