Number worksheet — GCSE Higher

1.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.

2.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

3.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

4.A charity bake sale sells 187 cakes at £2.95 each. By rounding each number to 1 significant figure, work out an estimate for the total amount raised.

5.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20

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

7.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

8.Oliver drives 95 km at an average speed of 50 km/h. Work out an estimate for the time the journey takes, by rounding the distance to the nearest 100 km.

9.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.

10.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

11.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

12.Work out ⁴√16

13.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.

14.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

15.Write 0.06 as a fraction in its simplest form.