Number worksheet — GCSE Higher

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

2.The length of a pencil is 8.4 cm, correct to 1 decimal place. Using L for the length of the pencil in centimetres, write down the error interval for L.

3.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

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

5.The rainfall in a town during April is recorded as 62.4 mm, correct to 1 decimal place. Write down the error interval for the actual rainfall, r mm.

6.A cube-shaped storage tank has a volume of 15,625 cubic centimetres. Work out the length of one edge of the tank.

7.A company's turnover is 5.6 × 10⁷ pounds, spread evenly across 3.5 × 10² shops. Work out the average turnover per shop, in standard form.

8.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.

9.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.

10.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.

12.A country has an area of 25,000,000 hectares. Write this area in standard form.

13.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

14.Simplify ⁴√(16a⁸b¹²)

15.A rectangular garden has a length of 12.4 m and a width of 7.5 m, each measured correct to 1 decimal place. Calculate the upper bound for the area of the garden.