Coaching Centre
Converting fractions, decimals and percentages
Converting between fractions, decimals and percentages, including terminating and recurring decimals.
Fractions and decimals
Some fractions give recurring decimals that repeat forever. Show this with a dot or bar: $\dfrac{1}{3} = 0.333\ldots = 0.\dot{3}$ and $\dfrac{2}{11} = 0.1818\ldots = 0.\overline{18}$.
Percentages
Per cent means "out of $100$".
Write $12.5\%$ as a fraction in simplest form.
Write $0.35$ as a simplified fraction.
$\tfrac{35}{100}$, divide by $5$.
Write $\dfrac{3}{8}$ as a decimal.
$3 \div 8$.
Write $\dfrac{3}{5}$ as a percentage (number only).
$\tfrac{3}{5} \times 100$.
Write $12.5\%$ as a simplified fraction.
$\tfrac{125}{1000}$.
Write $7\%$ as a decimal.
$7 \div 100$.
Which fraction gives a recurring decimal?
$0.666\ldots$
Write $1.45$ as a percentage (number only).
$1.45 \times 100$.
Which is the largest?
$0.72$ beats $0.7$ and $0.667$.
New numbers every time. Keep going until you get five in a row.