Number worksheet — GCSE Higher

1.Write down the exact decimal value of the fraction 1/6.

2.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.

3.The decimal 0.2333... has one non-recurring digit (the 2) followed by a single recurring digit (the 3), so it can be written as 0.2 recurring 3. Let x = 0.2333... . Work out x as a fraction in its simplest form.

4.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

5.Which of these decimals lies between 1/4 and 2/5?

6.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

7.Work out ∛(−27) + ∛8

8.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

9.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

10.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

11.Write 0.36 as a fraction in its simplest form.

12.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.

13.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

14.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

15.A jug holds 1.8 litres of juice. Priya pours out 3/4 of a litre to fill a glass. Work out how much juice is left in the jug, in millilitres.