Number worksheet — GCSE Higher

1.Write 5,000,000 in standard form.

2.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

3.Write these numbers in order, starting with the smallest: −1.4, 5/4, −6/5, 1.3, 0

4.2/3 of an amount of money is £30. Work out the amount.

5.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

6.A cube-shaped storage box has edges of length 7 cm. A shelf can hold a total volume of 2,000 cm³. Work out the greatest number of these boxes that will fit in that volume.

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

8.A jug holds 1.8 litres of juice. Priya pours out 3/4 of a litre to fill a glass. Work out how much juice is left in the jug, in millilitres.

9.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.

10.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

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

12.An allotment plot is divided into vegetables and flowers in the ratio 9 : 4. A third of the vegetable section is used for potatoes. What fraction of the whole plot is potatoes?

13.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

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

15.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.