GCSE Mathematics (9-1)
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    4.5 Recurring decimals — Practise with help

    Warm-up: remember

    Answer from memory before checking.

    1. From Section 4.4, write 0.1250.125 as a fraction in simplest form.
    2. From Section 4.4, write 38\frac{3}{8} as a decimal.
    Answers
    1. 18\frac{1}{8}.
    2. 0.3750.375.

    Practise with help

    Try each question first. Reveal the hint, next step and full working in that order.

    1. Convert 0.3˙0.\dot{3} to a fraction.

    Hint

    Let x=0.333…x=0.333\ldots and multiply by 1010.

    Next step

    Set up the calculation using that idea.

    Full working

    Then 10x=3.333…10x=3.333\ldots. Subtract to get 9x=39x=3, so x=13x=\frac{1}{3}.

    2. Convert 0.2˙7˙0.\dot{2}\dot{7} to a fraction.

    Hint

    Multiply by 100100 because the block has two digits.

    Next step

    Write the calculation before simplifying.

    Full working

    If x=0.272727…x=0.272727\ldots, then 100x−x=27100x-x=27, so 99x=2799x=27 and x=311x=\frac{3}{11}.

    3. Progress check. Convert 0.6˙0.\dot{6} to a fraction, then use it to find 0.6˙0.\dot{6} of £48.

    Hint

    First convert the recurring decimal to a fraction.

    Next step

    Then multiply £48 by that fraction.

    Full working

    0.6˙=230.\dot{6}=\frac23, so 23×£48=£32\frac23\times£48=£32.

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