Number worksheet — GCSE Higher

1.Write 7/12 as a decimal, showing clearly which digit is recurring.

2.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

3.Oliver drives 95 km at an average speed of 50 km/h. Work out an estimate for the time the journey takes, by rounding the distance to the nearest 100 km.

4.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

5.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².

6.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

7.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

8.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.

9.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

10.A recipe for one cake needs 2/3 of a cup of sugar. Priya has 3 1/2 cups of sugar. Work out how many complete cakes she can make.

11.Round 0.006852 to 2 significant figures.

12.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

13.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

14.Write 200 as a product of its prime factors, using index notation.

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