Number worksheet — GCSE Higher

1.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.

2.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

3.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

4.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

5.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

6.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

7.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.

8.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

9.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.

10.Work out 3³ + 2⁴.

11.A rectangular plywood panel measures 2.4 m by 0.75 m. Work out the area of the panel in square metres, giving your answer as a fraction in its simplest form.

12.Round 0.006482 to 2 significant figures.

13.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.

14.Work out √144 − 2 × 3 + √25

15.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.