Number worksheet — GCSE Higher

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

2.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

3.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.

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

5.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

6.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.

7.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?

8.Sam compares 0.6 and 5/8 by comparing the digit 6 with the digit 5, and says that 0.6 is the larger number. Convert 5/8 to a decimal to find the correct larger value.

9.2/3 of an amount of money is £30. Work out the amount.

10.A red blood cell has a diameter of about 7 × 10⁻⁶ metres. A virus has a diameter about 100 times smaller. Work out the diameter of the virus. Give your answer in standard form.

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

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

13.Work out 6² − 4².

14.Work out the value of 6² − 4³.

15.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.