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4 August, 02:40

How do you turn a decimal to a fraction

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  1. 4 August, 03:59
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    Say you have a number like

    12.34

    That is, 12 and 34 hundredths. 0.34 is the same as 34/100, so

    12.34 = 12 + 34/100 = 1200/100 + 34/100 = 1234/100 = 617/50

    If you have a number with repeating digits in the decimal, like

    12.343434 ... (with 34 repeating forever)

    we can let x be this number. Then

    100x = 1234.343434 ...

    If we subtract x from 100x, we can eliminate the repeating decimal part:

    100x - x = 1234.343434 ... - 12.343434 ...

    99x = 1234 - 12

    99x = 1222

    Then solving for x gives the decimal as a fraction:

    x = 1222/99
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