Number worksheet — GCSE Higher

1.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.

2.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

3.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

4.A jumper is reduced by 15% in a sale to a price of £42.50. Work out the original price.

5.Work out 10% of 30% of £200.

6.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³

7.A café orders 340 bread rolls at 24p each and 85 cakes at £1.35 each. Work out the total cost of the order.

8.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.

9.A train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.

10.A plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.

11.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

12.2/3 of an amount of money is £30. Work out the amount.

13.Work out (3 × 10²) × (2 × 10⁵). Give your answer in standard form.

14.A driving instructor is working out how many current-style UK number plates are possible. The format is 2 letters, then 2 digits, then a space, then 3 letters (for example AB12 CDE). The letters I, O and Q are never used in any letter position, leaving 23 allowed letters, but every letter and every digit may repeat anywhere on the plate. Work out how many different number plates are possible, giving your answer in standard form to 2 significant figures.

15.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56