Number worksheet — GCSE Higher

1.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.

2.A quantity surveyor calculates a length as 24.6851 m. Round this length to 2 decimal places.

3.A car travels 180 km using 6 litres of fuel. Work out the car's fuel consumption in kilometres per litre, then work out how many kilometres it can travel on a full tank of 12 litres at this rate.

4.The rainfall in a town during April is recorded as 62.4 mm, correct to 1 decimal place. Write down the error interval for the actual rainfall, r mm.

5.The length of a pencil is 8.4 cm, correct to 1 decimal place. Using L for the length of the pencil in centimetres, write down the error interval for L.

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

7.Petrol costs £1.48 per litre. Sam buys 35 litres and pays with three £20 notes. Work out his change.

8.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

9.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

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

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

12.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

13.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

14.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.

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