This topic summary covers Knowledge Organiser: FDP Conversions 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 15 of 15 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Knowledge Organiser: FDP Conversions
Key Terms
- FDP: Fractions, Decimals, Percentages — three ways to show the same amount
- Terminating decimal: Stops after a finite number of digits (e.g. 0.25)
- Recurring decimal: Repeats forever, shown with dots (e.g. 0.3̇ = 0.333…)
- Simplest form: A fraction where numerator and denominator share no common factors
Must-Know Equivalents
- 1/2 = 0.5 = 50%
- 1/4 = 0.25 = 25%; 3/4 = 0.75 = 75%
- 1/5 = 0.2 = 20%; 1/10 = 0.1 = 10%
- 1/3 = 0.333… = 33.3%; 2/3 = 0.666… = 66.7%
- 1/8 = 0.125 = 12.5%; 3/8 = 0.375 = 37.5%
- 0.5 = 50% (NOT 5%) — multiply by 100 to convert to %
Key Conversion Methods
- Fraction → Decimal: divide numerator by denominator
- Decimal → Fraction: write over power of 10, simplify
- Decimal → %: multiply by 100
- % → Decimal: divide by 100
- % → Fraction: write over 100, simplify
- Recurring → Fraction: use algebraic method (multiply by 10/100, subtract)
Common Mistakes
- Decimal to percentage: Multiply by 100, not divide — 0.5 = 50%, not 0.5%
- Percentage to decimal: Divide by 100 — 35% = 0.35, not 3.5
- Recurring decimals: Use dot notation correctly — 0.3̇ means 0.333…; 0.1̇2̇ means 0.121212…
- Not simplifying fractions: Always divide numerator and denominator by their HCF to give the answer in its simplest form
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!