Number worksheet — GCSE Higher

1.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?

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

3.Write down the reciprocal of 0.2

4.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.

5.Work out 6² − 4².

6.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

7.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.

8.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

9.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.

10.Write 0.005 in standard form.

11.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56

12.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.

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

14.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.

15.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².