Repeating decimals: sevenths, elevenths and the bar

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Learn it Some fractions make decimals that repeat forever. A bar goes over the digits that repeat. Elevenths repeat two digits (1/11 = 0.0909… = 0.0̅9̅), and sevenths repeat six digits (1/7 = 0.142857142857…). To turn a repeating decimal back into a fraction, put the repeating digits over 9s: one digit over 9, two digits over 99, three over 999, then reduce.

Example: Write 0.3̅6̅ as a fraction in lowest terms.

Two digits repeat, so put 36 over 99: 36/99.
Divide top and bottom by 9: 4/11.

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