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: \(\dfrac{2}{7} = 0.285\space714\space285\space714 … = 0.\overline{285\space714}\).