4.4 Fractions and terminating decimals — Learn

Prerequisites: multiplication and place value.

Objectives: Convert between terminating decimals and fractions, and work with these representations in calculations.

Learn the method

To convert a fraction to a decimal, divide the numerator by the denominator. To convert a terminating decimal, write it over $10$, $100$, or another power of $10$, then simplify. In simplest form, a fraction terminates exactly when its denominator has no prime factors other than $2$ and $5$.

Worked examples

Example 1. Write $\frac{7}{20}$ as a decimal.

Make the denominator $100$ by multiplying by $5$.

$\frac{7}{20}=\frac{35}{100}=0.35$.

Example 2. Write $0.125$ as a fraction.

There are three decimal places, so write it over $1000$.

$0.125=\frac{125}{1000}$.

Divide top and bottom by $125$.

$\frac{125}{1000}=\frac{1}{8}$.

Watch out. The decimal places set the denominator: $0.07=\frac{7}{100}$, not $\frac{7}{10}$. Count the places, then simplify and check by division.

Progress check

The discount is $\frac14=0.25=25\%$. The reduced price is $75\%$ of £48: $0.75\times48=£36$.

You should now be able to

• convert a terminating decimal to a fraction in simplest form;
• convert a fraction to a terminating decimal;
• recognise when a fraction has a terminating decimal;
• order decimals and fractions.

Covers: [N10].