Number worksheet — GCSE Higher

1.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.

2.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

3.Write 0.36 as a fraction in its simplest form.

4.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

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

6.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.

7.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

8.2/3 of an amount of money is £30. Work out the amount.

9.Estimate the value of √45, giving your answer to the nearest whole number.

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

11.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.

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.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

14.A café meal deal is one sandwich, one snack and one drink. There are 4 different sandwiches, 3 different snacks and 2 different drinks to choose from. Work out how many different meal deals are possible.

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