Number worksheet — GCSE Higher

1.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

2.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

3.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

4.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.

5.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

6.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

7.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

8.A measuring jug shows a volume of 340 ml, correct to the nearest 20 ml. Work out the smallest possible volume in the jug.

9.Simplify (3a²)² × (2a)³

10.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

11.In a youth club the number of girls is 2/3 of the number of boys. What fraction of the members of the club are girls?

12.Round 592.5 to the nearest 10.

13.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.

14.Expand and simplify √3(2 + √12).

15.Work out 4368 ÷ 12.