Converting Fractions, Decimals & Percentages (Cambridge (CIE) IGCSE Maths)

Revision Note

Written by: Mark Curtis

Reviewed by: Dan Finlay

Divide by 100 (move digits two places to the right)
- 6% as a decimal is 6 ÷ 100 = 0.06
- 40% as a decimal is 40 ÷ 100 = 0.4
- 350% as a decimal is 350 ÷ 100 = 3.5
- 0.2% as a decimal is 0.2 ÷ 100 = 0.002

Multiply by 100 (move digits two places to the left and add a % sign)
- 0.35 as a percentage is 0.35 × 100 = 35%
- 1.32 as a percentage is 1.32 × 100 = 132%
- 0.004 as a percentage is 0.004 × 100 = 0.4%

If it has one decimal place, write the digits over 10
- 0.3 is $\frac{3}{10}$
- 1.1 is $\frac{11}{10}$
If it has two decimal places, write the digits over 100
- 0.07 is $\frac{7}{100}$
- 0.13 is $\frac{13}{100}$
- 30.01 is $\frac{3001}{100}$
If it has n decimal places, write the digits over 10ⁿ
- 0.513 is $\frac{513}{1000}$
- 0.0007 is $\frac{7}{10 000}$
Learn simple recurring decimals as fractions
- 0.33333… = $0 . \dot{3}$ is $\frac{1}{3}$
- 0.66666… = $0 . \dot{6}$ is $\frac{2}{3}$
Whole numbers can be written as fractions by writing them over 1
- 5 is $\frac{5}{1}$

$converting between fractions and decimals$

Fractions written over powers of 10 are quicker
- $\frac{3}{5} = \frac{6}{10}$ which is 0.6
- $\frac{7}{20} = \frac{35}{100}$ which is 0.35
- $\frac{1}{500} = \frac{2}{1000}$ which is 0.002

Change fractions into decimals then multiply by 100
- $\frac{4}{5} = \frac{8}{10}$ which is 0.8 as a decimal, which is 0.8 × 100 = 80%

A calculator can be used to check conversions between fractions and decimals (even if the question says to show working without a calculator)

Last updated: 14 May 2024

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