Fractions, Decimals and Percentages Together

What you will learn

• Convert between fractions, decimals and percentages.
• Remember the common equivalents.
• Compare and order numbers written in different forms.

Before you start: you should know what a percentage is and how to turn a fraction into a decimal. See Percentages and Decimals Explained.

The idea

$\frac{3}{5}$, $0.6$ and $60\%$ all name the same amount. Which form you use depends on the job: fractions for sharing, decimals for calculators and measuring, percentages for comparing.

The three conversions

• Fraction to decimal: divide the top by the bottom.
• Decimal to percentage: multiply by $100$.
• Percentage to fraction: write it over $100$ and simplify.

Going the other way, divide a percentage by $100$ to get a decimal.

Learn these

On the number line

All three forms share one number line from $0$ to $1$ (or $0\%$ to $100\%$).

Comparing

To compare numbers in different forms, change them all to decimals (or all to percentages), then compare.

Worked examples

Example 1: Fraction to percentage

Write $\frac{7}{8}$ as a decimal and as a percentage.

1. $7 \div 8 = 0.875$.
2. $0.875 \times 100 = 87.5$.

Answer: $0.875$ and $87.5\%$.

Example 2: Percentage to fraction

Write $64\%$ as a fraction in its simplest form.

1. $64\% = \frac{64}{100}$.
2. Divide top and bottom by $4$: $\frac{16}{25}$.

Answer: $\frac{16}{25}$

Example 3: Put in order

Order $\frac{3}{5}$, $0.58$ and $61\%$, smallest first.

1. As percentages: $60\%$, $58\%$ and $61\%$.
2. Smallest to largest: $58\%$, $60\%$, $61\%$.

Answer: $0.58$, $\frac{3}{5}$, $61\%$

Tip: some fractions, like $\frac{1}{3}$, do not make a neat decimal: $0.333\ldots$ is about $33.3\%$.

Why it matters

Shop offers, test scores, recipes and weather reports each prefer one form. Being able to switch between them lets you compare a $\frac{1}{3}$ off deal with a $30\%$ off deal and see which is better.