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.

What Is FDP Conversion?

Fractions, decimals, and percentages are three different ways of expressing the same value. Being able to move fluently between them lets you choose the most convenient form for a given calculation or comparison.

Key equivalences you should memorise include: 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%, and 1/3 = 0.333... = 33.3...%.

Understanding these conversions also helps with ordering and comparing values — a common exam question type.

Key Formulas

Step-by-Step Method

1. Fraction to decimal: Divide the numerator by the denominator (e.g. 3/8 = 3 ÷ 8 = 0.375).
2. Decimal to percentage: Multiply by 100 (e.g. 0.375 × 100 = 37.5%).
3. Percentage to decimal: Divide by 100 (e.g. 37.5 ÷ 100 = 0.375).
4. Percentage to fraction: Write the percentage over 100 and simplify (e.g. 37.5% = 375/1000 = 3/8).
5. 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 1 — Foundation Level

Question: Convert 7/20 to a decimal and a percentage.

Working:

Step 1 — Fraction to decimal: 7 ÷ 20 = 0.35.

Step 2 — Decimal to percentage: 0.35 × 100 = 35%.

Answer: 7/20 = 0.35 = 35%

Worked Example 2 — Higher Level

Question: Put these values in order from smallest to largest: 0.62, 3/5, 63%.

Working:

Step 1 — Convert all to decimals: 0.62 stays as 0.62. 3/5 = 3 ÷ 5 = 0.6. 63% = 63 ÷ 100 = 0.63.

Step 2 — Order the decimals: 0.6, 0.62, 0.63.

Answer: 3/5, 0.62, 63%

Worked Example 3 — Exam Style

Question: A student scores 17 out of 25 on a test. Express this as a percentage.

Working:

Step 1 — Write as a fraction: 17/25.

Step 2 — Convert to a decimal: 17 ÷ 25 = 0.68.

Step 3 — Multiply by 100: 0.68 × 100 = 68%.

Answer: 68%

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.

Practice Questions

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.

Practise converting fractions, decimals and percentages questions with instant feedback — completely free on GCSEMathsAI.

Related Topics

• Fractions
• Decimals
• Percentages

Summary

• Fractions, decimals, and percentages are three forms of the same value.
• Fraction to decimal: divide numerator by denominator.
• Decimal to percentage: multiply by 100.
• Percentage to fraction: write over 100 and simplify.
• Memorise common equivalences to save time in exams.