# Periodic Number

## Periodic Number

Expression used to refer to a number whose decimal notation is repeating. It includes rational numbers where the decimal expansion does not have 0 or 9 as a period.

### Symbol

The period of a number with a repeating decimal is noted with a horizontal line above the sequence of digits that repeats:
$$\dfrac{2}{13} = 0.153\space846\space153\space846 … = 0.\overline{153\space846}$$

### Examples

• The number $$\dfrac{3}{11}$$ is a periodic number where the period is 27, because: $$\dfrac{3}{11} = 0.272\space727\space272 … = 0.\overline{27}$$.
• The number $$\dfrac{2}{7}$$ is a periodic number where the period is 285 714, because: $$\dfrac{2}{7} = 0.285\space714\space285\space714 … = 0.\overline{285\space714}$$.