Skip to content
MathAnvil
§ Fractions

Fraction / Decimal / Percent

§ Fractions

Fraction / Decimal / Percent

CCSS.6.RPCCSS.7.NS3 min read

Fractions, decimals, and percentages represent identical mathematical values expressed in different forms. Converting between these three representations requires understanding that 1/4, 0.25, and 25% all describe precisely the same quantity. The UK National Curriculum emphasises these equivalences from Year 6, where pupils recall and use connections between fractions, decimals, and percentages.

§ 01

Why it matters

These conversions appear throughout real-world scenarios involving proportions and comparisons. Shop discounts display as percentages (30% off), bank interest rates show as decimals (0.045), and recipe measurements use fractions (34 cup). GCSE mathematics papers frequently test these conversions across multiple topics including ratio, probability, and statistics. Financial literacy depends on recognising that 0.15 interest rate equals 15% annually. Scientific data often requires switching between decimal measurements (0.375 metres) and fractional equivalents (38 metre). Understanding these relationships builds foundation skills for advanced topics like compound percentage calculations, standard form notation, and trigonometric ratios in further mathematics studies.

§ 02

How to solve fraction / decimal / percent

Fraction / Decimal / Percent

  • Fraction → decimal: divide numerator by denominator.
  • Decimal → percent: multiply by 100.
  • Percent → fraction: write over 100, simplify.

Example: 38 → 0.375 → 37.5%.

§ 03

Worked examples

Beginner§ 01

Convert 14 to a decimal.

Answer: 0.25

  1. Divide numerator by denominator → 1 ÷ 4 = 0.25 — Fraction means division.
  2. Verify → 14 = 0.25 ✓ — Check.
Easy§ 02

Convert 12 to a percent.

Answer: 50%

  1. Divide then multiply by 100 → 1 ÷ 2 × 100 = 50% — Fraction → decimal → percent.
  2. Verify → 12 = 50% ✓ — Check.
Medium§ 03

Convert 0.2727 to a fraction.

Answer: 311

  1. Write as fraction over power of 10 → 0.2727 → 311 — Then simplify.
  2. Verify → 311 ✓ — Check.
§ 04

Common mistakes

  • Converting fractions to percentages by multiplying the numerator alone, writing 3/4 as 300% instead of 75%
  • Placing decimal points incorrectly when converting percentages, writing 35% as 3.5 instead of 0.35
  • Forgetting to simplify final fraction answers, leaving 25/100 instead of reducing to 1/4
§ 05

Frequently asked questions

How do you convert a fraction to a decimal?
Divide the numerator by the denominator. For 3/8, calculate 3 ÷ 8 = 0.375. This works because fractions represent division problems, so 3/8 literally means '3 divided by 8'.
What's the quickest way to convert decimals to percentages?
Multiply the decimal by 100 and add the percentage symbol. For 0.45, calculate 0.45 × 100 = 45%. This works because 'percent' means 'per hundred', so multiplying by 100 shows how many parts per 100.
How do you turn a percentage into a fraction?
Write the percentage number over 100, then simplify. For 60%, write 60/100, then reduce by dividing both parts by their highest common factor (20) to get 3/5.
Why do some fractions give recurring decimals?
When the denominator contains prime factors other than 2 and 5, the decimal repeats. For example, 1/3 = 0.333... because 3 doesn't divide evenly into powers of 10. Only fractions with denominators containing just 2s and 5s terminate.
Which percentage calculations appear most in GCSE exams?
Percentage increase and decrease problems dominate GCSE papers, often involving VAT (20%), discounts (15-30%), and compound interest. Converting between the three forms frequently appears in probability questions and statistical analysis tasks.
§ 06

See also

MultipleRatioProbabilityPercentageFractionNumeratorDenominatorFactor
§ 06

Where to next?

Share this article