Number worksheet — GCSE Higher

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

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

3.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.

4.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.

5.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?

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

7.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

8.A plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.

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

10.Work out ∛(−27) + ∛8

11.Work out the exact value of √(2² + 3²)

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

13.Work out −4.5 + 2.8.

14.The recurring decimal 0.454545... can be written as 0.45 recurring, where both digits repeat forever. Let x = 0.45 recurring. Work out x as a fraction in its simplest form.

15.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.