Sheet № 126 · Foundation + Higher · AQA · Edexcel · OCR
Converting Fractions, Decimals and Percentages –
Converting between fractions, decimals, and percentages (often called FDP) is a fundamental GCSE Maths skill. Questions testing this appear on both Foundation and Higher papers and are often embedded within larger problems on probability, proportion, and data.
§Key definitions
Question:
Convert 7/20 to a decimal and a percentage.
Answer:
7/20 = 0.35 = 35%
Q1 (Foundation):
Convert 0.45 to a fraction in its simplest form.
Q2 (Foundation):
Convert 3/8 to a percentage.
Q3 (Higher):
Put in order from smallest to largest: 7/12, 58%, 0.583.
§Formulas to memorise
Fraction → Decimal: divide the numerator by the denominator
Decimal → Percentage: multiply by 100
Percentage → Fraction: write over 100 and simplify
Fraction to decimal: — Divide the numerator by the denominator (e.g. 3/8 = 3 ÷ 8 = 0.375).
Decimal to percentage: — Multiply by 100 (e.g. 0.375 × 100 = 37.5%).
Percentage to decimal: — Divide by 100 (e.g. 37.5 ÷ 100 = 0.375).
Percentage to fraction: — Write the percentage over 100 and simplify (e.g. 37.5% = 375/1000 = 3/8).
Decimal to fraction: — Write as a fraction over the appropriate power of 10 and simplify (e.g. 0.375 = 375/1000 = 3/8).
Worked example
Convert 7/20 to a decimal and a percentage.
Working:
⚠ Common mistakes
- ✗Dividing the wrong way round. To convert a fraction to a decimal, divide the numerator by the denominator — not the other way around.
- ✗Forgetting to simplify when converting a percentage to a fraction. Always reduce the fraction to its simplest form.
- ✗Moving the decimal point the wrong number of places. When converting between decimals and percentages, the decimal point moves exactly two places.
✦ Exam tips
- →Memorise the common equivalences (halves, quarters, fifths, eighths, tenths) — they save time in the exam.
- →When ordering mixed FDP values, convert everything to the same form — decimals are usually easiest.
- →On non-calculator papers, use equivalent fractions to convert to a denominator of 10, 100, or 1000 where possible.