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Higher Level: Recurring Decimals to Fractions

Part of FDP Conversions — GCSE Mathematics

This deep dive covers Higher Level: Recurring Decimals to Fractions within FDP Conversions for GCSE Mathematics. Revise FDP Conversions in Number for GCSE Mathematics with 12 exam-style questions and 22 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 11 of 14 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 11 of 14

Practice

12 questions

Recall

22 flashcards

Higher Level: Recurring Decimals to Fractions

To convert 0.363636... to a fraction:

  1. Let x = 0.363636...
  2. Multiply by 100: 100x = 36.363636...
  3. Subtract: 100x - x = 36
  4. Solve: 99x = 36, so x = 36/99
  5. Simplify: 36/99 = 4/11

Pattern: For 0.ababab... use 99 in denominator

For 0.abcabc... use 999 in denominator

Keep building this topic

Read this section alongside the surrounding pages in FDP Conversions. That gives you the full topic sequence instead of a single isolated revision point.

Worked Example 4: Ordering Mixed FDPQuick Conversion TricksThree Ways to Show the Same ThingThe FDP Triangle

Practice Questions for FDP Conversions

Which decimal is equal to 3/4?

  • A. 0.34
  • B. 0.75
  • C. 0.43
  • D. 1.33
1 markfoundation

Explain why 1/3 cannot be written as an exact decimal, and write 1/3 using correct notation for recurring decimals.

2 marksstandard

Quick Recall Flashcards

FDP Triangle
F (top) D (left) ← → P (right) F→D: divide F→P: ×100 D→P: ×100
Halves family
1/2 = 0.5 = 50% Must know instantly!

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Worked Example 4: Ordering Mixed FDP

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Quick Conversion Tricks