Number worksheet — GCSE Foundation

1.To estimate the cost of buying 38.7 m of rope at £21.40 per metre, both numbers are first rounded to 1 significant figure. Work out the estimate.

2.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.

3.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

4.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.

5.A charity raises 8 × 10⁶ pounds. This total is shared equally among 2 × 10² local projects. Work out how much each project receives, in standard form.

6.Write 45,000 in standard form.

7.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

8.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

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 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 number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

12.Sam rounds 0.070268 to 3 significant figures and writes 0.0703. Which of these statements is correct?

13.A block of butter has a mass of 250 g, correct to the nearest 10 g. Using m for the mass of the block in grams, write down the error interval for m.

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

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