Number worksheet — GCSE Higher

1.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.

2.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.

3.A washing machine costs £320 before VAT. VAT is charged at 20%. Work out the total price including VAT.

4.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

5.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.

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

7.Work out (4 × 10³) × (3 × 10¹). Give your answer in standard form.

8.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.

9.The number of visitors to a museum on Saturday is given as 1,800, correct to the nearest 100. Which of these could not be the actual number of visitors?

10.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

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

12.Four locations each record a temperature one winter morning. Which of these temperatures is the coldest?

13.Maya buys 4 plants at £3.20 each and a bag of compost for £6.75. She pays with a £20 note. Work out her change.

14.A company's turnover is 5.6 × 10⁷ pounds, spread evenly across 3.5 × 10² shops. Work out the average turnover per shop, in standard form.

15.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2