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Recurring Decimals Calculator

Turn any recurring decimal into an exact fraction with the classic algebra proof: call it x, multiply by powers of ten until the repeating tails line up, subtract, and the tail vanishes. Every line of that argument is shown, then the fraction is simplified and checked.

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    Worked Example

    Write 0.3636... as a fraction in its simplest form.

    1. Call it x:x = 0.3636...
    2. Multiply by 100 so one repeat crosses the point:100x = 36.3636...
    3. Subtract:99x = 36, so x = 3699
    4. Simplify by dividing by 9:x = 411

    Answer: 411

    Try These Yourself

    Write 0.777... as a fraction.Show answerHide answer

    Answer: 79

    10x − x = 9x = 7.

    Write 0.1666... as a fraction.Show answerHide answer

    Answer: 16

    100x − 10x = 90x = 15, so x = 1590.

    Write 0.454545... as a fraction.Show answerHide answer

    Answer: 511

    99x = 45, then divide top and bottom by 9.