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: [latex]\dfrac{2}{13} = 0.153\space846\space153\space846 ... = 0.\overline{153\space846}[/latex]Examples
- The number [latex]\dfrac{3}{11}[/latex] is a periodic number where the period is 27, because: [latex]\dfrac{3}{11} = 0.272\space727\space272 ... = 0.\overline{27}[/latex].
- The number [latex]\dfrac{2}{7}[/latex] is a periodic number where the period is 285 714, because: [latex]\dfrac{2}{7} = 0.285\space714\space285\space714 ... = 0.\overline{285\space714}[/latex].