Number worksheet — GCSE Higher

1.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.

2.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

3.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

4.Simplify (x⁻²)³, giving your answer as a fraction.

5.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?

6.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?

7.Work out the value of √(16 + 9)

8.Which of these is written correctly in standard form?

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

10.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.

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

12.Simplify (3a²)² × (2a)³

13.Given that 2⁵ = 32, work out 2⁶.

14.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

15.Write these numbers in order, starting with the smallest: −1.4, 5/4, −6/5, 1.3, 0