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Let x be the recurring decimal.

Mathematics

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3. Convert the recurring decimal 12.18‾12.1\overline{8} into fraction

  1. Let xx be the recurring decimal.

    x=12.18‾x = 12.1\overline{8}

  2. Multiply by 10 to move the non-repeating part to the left of the decimal point.

    10x=121.8‾(∗)10x = 121.\overline{8} \quad (*)

  3. Multiply by 10 again to move one cycle of the repeating part to the left of the decimal point.

    100x=1218.8‾(∗∗)100x = 1218.\overline{8} \quad (**)

  4. Subtract equation (∗)(*)

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