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Fractions, Decimals and Percentages: How to Convert Them

Switch between fractions, decimals and percentages, including recurring decimals, with worked examples and practice questions to check your answers.

  • ⏱ 3 min read
  • ✏️ 3 worked examples
  • 🎯 5 practice questions
  • 📶 Beginner
KS3GCSEMiddle SchoolHigh School
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Curriculum fit: GCSE Maths Number (Foundation and Higher; recurring decimal to fraction is Higher). US: Grade 6-7 rational numbers.

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What Is It?

Fractions, decimals and percentages are three ways of writing the same value. For example, 1/4, 0.25 and 25% are all equal. Being able to switch between them helps you compare amounts and solve problems quickly.

Some fractions give decimals that never end, such as 1/3 = 0.333... These are recurring decimals.

Fraction3/4Decimal0.75Percentage75%top ÷ bottom× 100÷ 100Percentage to fraction: write over 100, then simplify75% = 75/100 = 3/4
The same amount can be written three ways. Learn the common conversions, and use division and multiplying or dividing by 100 for the others.

Key Formulas and Ideas

  • Fraction to decimal: divide the numerator by the denominator.
  • Decimal to percentage: multiply by 100. Percentage to decimal: divide by 100.
  • Percentage to fraction: write over 100 and simplify.

Worked Examples

Example 1

Fraction to Decimal and Percentage

Question

Write 3/8 as a decimal and a percentage.

  1. Divide 3 by 8: 0.375.
  2. Multiply by 100: 37.5%.

✓ Answer 0.375 and 37.5%

Example 2

Percentage to Fraction

Question

Write 45% as a fraction in its simplest form.

  1. 45% = 45/100.
  2. Divide top and bottom by 5: 9/20.

✓ Answer 9/20

Example 3

Recurring Decimal to Fraction (Higher)

Question

Write 0.4545... (45 recurring) as a fraction.

  1. Let x = 0.4545...
  2. Multiply by 100: 100x = 45.4545...
  3. Subtract: 99x = 45.
  4. x = 45/99 = 5/11.

✓ Answer 5/11

Common Mistakes to Avoid

  • Writing 1/4 as 1.4 or 0.4. Divide 1 by 4 to get 0.25.
  • Forgetting to simplify fractions.
  • Rounding a recurring decimal and treating it as exact.
  • Moving the decimal point the wrong way when changing between decimals and percentages.

Practice Questions

0 of 5 answered
Q1Write 0.6 as a percentage.
Q2Write 7/20 as a decimal.
Q3Write 12.5% as a fraction.
Q4Which is largest: 0.4, 3/8 or 41%?
Q5Write 2/3 as a decimal.

Frequently Asked Questions

Which fractions give recurring decimals?

When the denominator in simplest form has a prime factor other than 2 or 5, the decimal recurs. For example 1/3 and 1/7 recur, but 1/8 does not.

How do I order a mixed set of fractions, decimals and percentages?

Convert them all to decimals, then compare.

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Sources and Review

Reviewed by StudyMorrow editorial review on 5 Nov 2026.