Terminating decimals, fractions and percentages

Moving between fractions, decimals and percentages, including values bigger than 1 and bigger than 100%, lets you compare anything.

Practise this lesson free (7 questions)

Decimals to fractions

Use place value, then simplify.
0.65 = 65100 = 1320
0.375 = 3751000 = 38
2.4 = 2410 = 125

Which fractions terminate?

A terminating decimal stops, such as 720 = 0.35.
A fraction in its simplest form terminates only when its denominator has no prime factors except 2 and 5.
20 = 22 × 5, so 720 terminates. 3 is not 2 or 5, so 13 = 0.333... recurs (repeats forever).

One quantity as a fraction or percentage of another

Write it as a fraction, then convert.
45 out of 60 = 4560 = 34 = 75%
The answer can be bigger than 1: 30 compared with 24 is 3024 = 54 = 1.25 = 125%.
150% of 40 = 1.5 × 40 = 60.
Worked example

Write 58, 0.6, 63% and 0.62 in order, smallest first.

  1. 58 = 0.625 and 63% = 0.63
  2. As decimals: 0.625, 0.6, 0.63, 0.62
  3. Order: 0.6, 0.62, 0.625, 0.63

Answer: 0.6, 0.62, 58, 63%

Key idea

Decimals become fractions over 10, 100 or 1 000, then simplify. Simplest-form fractions terminate only if the denominator uses just 2s and 5s. Fractions and percentages can be greater than 1 and 100%.

Key words
Simplify
Write in the simplest form: collect like terms, or divide a fraction or ratio by a common factor.
Denominator
The bottom number of a fraction. It shows how many equal parts the whole is split into.

All KS3 Mathematics key terms and definitions →

Common mistakes
Quick check

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Extra practice

2 more questions

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  1. Write 0.85 as a fraction. Give your answer as a fraction in its simplest form.

    Show the answer

    Answer: 17/20

    0.85 = 85100 = 1720.

  2. Write 0.625 as a fraction. Give your answer as a fraction in its simplest form.

    Show the answer

    Answer: 5/8

    0.625 = 6251000 = 58.

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Practise this lesson free (7 questions)All KS3 Mathematics lessons

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Sources and references

Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.