GCSE Maths (Edexcel)

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Converting from a Recurring Decimal

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Number Fractions, Decimals and Percentages

Converting from a Recurring Decimal

6:12 Recurrign Decimals
Spec N10
Previous Converting to a Recurring Decimal Next Recurring Decimals
  • Recurring decimals can be converted to fractions by eliminating repeated digits
  • Multiplication can be used to find a number with the same decimal pattern
  • Multiply by 10 if one digit recurs, multiply by 100 if two digits recur, etc.
  • Example: converting 0.6 recurring to a fraction
  • Set 0.6 recurring equal to x
  • Multiply both sides by 10
  • Subtract the original equation from the new equation
  • Rearrange to make x the subject and simplify if possible
  • Multiplying by 10 won't always work if there is a decimal digit before recurring digits
  • Example: converting 0.473 recurring to a fraction
  • Multiply by 10 and 1000 to eliminate recurring digits
  • Subtract the original equation from the new equation
  • Rearrange to make x the subject and simplify if possible

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