Converting Fractions, Decimals and Percentages

📋 Spec coverage: GCSE Edexcel Mathematics (1MA1) This article covers Edexcel N10 (1.4.1): working interchangeably with terminating decimals and fractions, and the fraction-decimal-percentage conversion element of Edexcel R9 (3.3.1). This applies to Foundation and Higher tiers and may be assessed on any of the three papers.

To convert between fractions, decimals and percentages, use division, multiplication by $100$, or place value.

The conversion methods

A numerator is the top number of a fraction, while the denominator is the bottom number.

• Fraction to decimal: divide the numerator by the denominator.

$$\frac{3}{8}=3÷8=0.375$$

• Decimal to percentage: multiply by $100$.

$$0.375\times 100=37.5\%$$

• Percentage to decimal: divide by $100$.

$$62\%÷100=0.62$$

• Decimal to fraction: use place value, then simplify. For example, $0.45$ means $45$ hundredths:

$$0.45=\frac{45}{100}=\frac{9}{20}$$

• Percentage to fraction: write the percentage over $100$, then simplify.

$$35\%=\frac{35}{100}=\frac{7}{20}$$

• Fraction to percentage: divide to obtain a decimal, then multiply by $100$.

Worked example

Convert $\frac{3}{8}$ into a decimal and a percentage.

First, divide the numerator by the denominator:

$$3÷8=0.375$$

Then multiply the decimal by $100$:

$$0.375\times 100=37.5\%$$

Therefore:

$$\frac{3}{8}=0.375=37.5\%$$

You can check the result using the known fraction $\frac{3}{4}=75\%$. Since $\frac{3}{8}$ is half of $\frac{3}{4}$, its percentage should be half of $75\%$, which is $37.5\%$.

Useful conversions to remember

Some common equivalents can save time:

• One half is $0.5=50\%$.
• One quarter is $0.25=25\%$.
• Three quarters is $0.75=75\%$.
• One fifth is $0.2=20\%$.

Use these as checks, but show division or place-value working when the conversion is less familiar.

Common exam mistake

Do not multiply by $100$ when converting a percentage to a decimal. Move from percentage to decimal by dividing by $100$. For example:

$$7\%=0.07$$

Check whether your answer is sensible: a percentage below $100\%$ gives a decimal below $1$, while a percentage above $100\%$ gives a decimal above $1$.

Completeness check: Terminating fraction-decimal conversions are fully covered. The relevant R9 conversion skill is covered; wider R9 topics such as percentage change, original values and simple interest are outside this question.