Number worksheet — GCSE Higher

2.Write 0.06 as a fraction in its simplest form.

3.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

4.Work out ⁴√81

5.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

6.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

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.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.

9.Work out the value of √49 + ∛27

10.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?

11.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.

12.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

13.To estimate the cost of buying 38.7 m of rope at £21.40 per metre, both numbers are first rounded to 1 significant figure. Work out the estimate.

14.Find the missing number: ▢ ÷ 15 = 24

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