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: \(\dfrac{2}{27}=0.074074074\ldots=0.\overline {074}\).