Number worksheet — GCSE Higher

1.A charity bake sale sells 187 cakes at £2.95 each. By rounding each number to 1 significant figure, work out an estimate for the total amount raised.

2.Write 5,000,000 in standard form.

3.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

4.Work out (−2)³ + (−3)² − (−4)

5.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.

6.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

7.Simplify x⁷ × x⁴, giving your answer as a single power of x.

8.A car travels 180 km using 6 litres of fuel. Work out the car's fuel consumption in kilometres per litre, then work out how many kilometres it can travel on a full tank of 12 litres at this rate.

9.Work out (−36) ÷ (−6) × 2

10.Write these numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09

11.Simplify (3a²)² × (2a)³

12.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.

13.Work out (4 × 10³) × (3 × 10¹). Give your answer in standard form.

14.Round 592.5 to the nearest 10.

15.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?