Number worksheet — GCSE Higher

1.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

2.The recurring decimal 0.454545... can be written as 0.45 recurring, where both digits repeat forever. Let x = 0.45 recurring. Work out x as a fraction in its simplest form.

3.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

4.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.

5.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

6.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².

7.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

8.Work out √225 ÷ 3.

9.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

10.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.

11.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.

12.Estimate the value of √45, giving your answer to the nearest whole number.

13.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.

14.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.

15.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.