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 15 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Higher Level: Recurring Decimals to Fractions
To convert 0.363636... to a fraction:
- Let x = 0.363636...
- Multiply by 100: 100x = 36.363636...
- Subtract: 100x - x = 36
- Solve: 99x = 36, so x = 36/99
- Simplify: 36/99 = 4/11
Pattern: For 0.ababab... use 99 in denominator
For 0.abcabc... use 999 in denominator
Practice questions for FDP Conversions
Which decimal is equal to 3/4?
Explain why 1/3 cannot be written as an exact decimal, and write 1/3 using correct notation for recurring decimals.
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!