Number worksheet — GCSE Higher

1.Work out 36 ÷ (2 × 3)

2.Simplify (3a²)² × (2a)³

3.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.

4.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.

5.Find the missing number: 17 × ▢ = 391

6.A crowd of 8,400 people is recorded correct to the nearest 100. Work out the smallest possible number of people in the crowd.

7.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

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

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

10.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.

11.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

12.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

13.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.

14.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

15.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.