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MathidiaMathematics Academy
Decimals and percentages
Lesson 27 of 75
Easy practice

Fractions and decimals

Objective. Convert common fractions to terminating decimals and back.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

A fraction can be written as a decimal by dividing the numerator by the denominator, and a terminating decimal can be converted back to a fraction using place value. For example, 3/4 becomes 0.75 because 3÷4=0.75. Going the other way, 0.6 is 6 tenths, written as 6/10, which simplifies to 3/5. Fractions with denominators that only have 2s and 5s as factors, such as 4, 5, 8 or 20, always give terminating decimals, while others like 1/3 give recurring decimals. Simplifying the fraction after conversion is essential for a fully correct answer.

Worked example

Convert 0.35 to a fraction in its simplest form.

0.35
Illustrated card showing 0.35
  1. 1Write 0.35 using place value: 35/100.
  2. 2Find the HCF of 35 and 100, which is 5.
  3. 3Divide both parts by 5: 35÷5=7, 100÷5=20.
  4. 4Check 7 and 20 share no common factor, giving the simplest form.

Answer: 7/20

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Practice

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Common mistake. Pupils sometimes write 0.4 as 4/100 instead of 4/10, confusing tenths with hundredths. Always count the decimal places to identify the correct place value denominator.

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