AI generatedNumberGCSE Higher

Mixed recurring decimals to fractions

First multiply by a power of 10 to move the non-repeating digits to the left of the decimal point.

  • First multiply by a power of 10 to move the non-repeating digits to the left of the decimal point.
  • Multiply again to shift one whole repeating block. Subtract equations with identical recurring tails.
  • Divide by the resulting coefficient of and simplify the fraction.

Example 1

Write the recurring decimal as a fraction in simplest form.

Let be the decimal.Shift the non-repeating digit.Shift one whole two-digit block.Subtract from ; the infinite tails cancel.Divide both sides by 990.

Example 2

Write the recurring decimal as a fraction in simplest form.

Let be the decimal.Shift the non-repeating digit.Shift one whole two-digit block.Subtract from ; the infinite tails cancel.Divide both sides by 990.

Remember
Use the worked steps to check your method, not just the final answer.

Your turn

Question 1

Write the recurring decimal as a fraction in simplest form.

Check answer
Let be the decimal.Shift the non-repeating digit.Shift one whole two-digit block.Subtract from ; the infinite tails cancel.Divide both sides by 990.
Question 2

Write the recurring decimal as a fraction in simplest form.

Check answer
Let be the decimal.Shift the non-repeating digit.Shift one whole two-digit block.Subtract from ; the infinite tails cancel.Divide both sides by 990.
Question 3

Write the recurring decimal as a fraction in simplest form.

Check answer
Let be the decimal.Shift the non-repeating digit.Shift one whole two-digit block.Subtract from ; the infinite tails cancel.Divide both sides by 990.
Question 4

Write the recurring decimal as a fraction in simplest form.

Check answer
Let be the decimal.Shift the non-repeating digit.Shift one whole two-digit block.Subtract from ; the infinite tails cancel.Divide both sides by 990.
Question 5

Write the recurring decimal as a fraction in simplest form.

Check answer
Let be the decimal.Shift the non-repeating digit.Shift one whole two-digit block.Subtract from ; the infinite tails cancel.Divide both sides by 990.
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