Number worksheet — GCSE Higher

1.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.

2.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.

3.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

4.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.

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

6.Work out √3 × √12, giving your answer as an integer.

7.A florist has 5 different flowers. Freya picks 3 of them to make a small bunch, and the order in which she picks them does not matter. Work out how many different bunches she could make.

8.Write down the symbol that makes this statement true: −2/3 ___ −5/6

9.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

10.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

11.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

12.An allotment is divided into two plots in the ratio 2:3. The larger plot has an area of 18 m². Work out the fraction of the total area taken up by the smaller plot.

13.Work out 5⁰ + 5¹ + 5²

14.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.

15.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.