Write \( \dfrac{3}{8} \) as a decimal and as a percentage.
\( 3 \div 8 = 0.375 \). As a percentage: \( 37.5\% \).
Fractions, Decimals & Percentages
10 exam-style questions on conversions, percentage of amounts, percentage change and reverse percentages. Tap Show answer for full working.
4 Easy 4 Medium 2 Hard
Find \( 15\% \) of \( 240 \).
\( 10\% \) of \( 240 = 24 \), so \( 5\% = 12 \). \( 15\% = 24 + 12 = 36 \).
Write \( 0.36 \) as a fraction in its simplest form.
\( 0.36 = \dfrac{36}{100} = \dfrac{9}{25} \).
A jacket costs £80. In a sale it is reduced by \( 20\% \). What is the sale price?
\( 20\% \) of \( 80 = 16 \). Sale price \( = 80 - 16 = £64 \).
A population increases from \( 12\,000 \) to \( 13\,800 \). Calculate the percentage increase.
Increase \( = 13800 - 12000 = 1800 \). Percentage increase \( = \dfrac{1800}{12000} \times 100 = 15\% \).
After a \( 12\% \) increase, a laptop costs £448. Find the original price.
New price is \( 112\% \) of original. \( 448 \div 1.12 = 400 \). Original price \( = £400 \).
Calculate \( \dfrac{2}{5} \) of \( 3.5 \) kg. Give your answer in grams.
\( \dfrac{2}{5} \times 3.5 = 1.4 \) kg \( = 1400 \) g.
A shop offers \( 15\% \) off all items. A coat is reduced by £18. What was the original price of the coat?
\( 15\% \) of original \( = 18 \). Original \( = 18 \div 0.15 = £120 \).
A car is worth £9000. It depreciates by \( 20\% \) in the first year and \( 15\% \) in the second year. Find its value after two years.
After year 1: \( 9000 \times 0.8 = 7200 \). After year 2: \( 7200 \times 0.85 = 6120 \). Value \( = £6120 \).
In a sale, prices are reduced by \( 25\% \). After the sale, prices increase by \( 20\% \). Is the final price higher or lower than the original, and by what percentage?
Multiplier: \( 0.75 \times 1.20 = 0.9 \). Final price is \( 90\% \) of original — \( 10\% \) lower.