Number worksheet — GCSE Foundation

1.Write 0.00072 in standard form.

2.Write these numbers in order, starting with the smallest: 3, −1, 0, −5

3.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.

4.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

5.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

6.Simplify (y³)⁴, giving your answer as a single power of y.

7.Write 0.45 as a fraction in its simplest form.

8.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.

9.A bag holds 50 counters. 2/5 of them are red and the rest are blue. 5 red counters are then taken out of the bag. Work out the new ratio of red counters to blue counters. Give your answer in its simplest form.

10.Grace drinks 1/3 of a bottle of water in the morning and another 1/3 of the same bottle in the afternoon. Work out what fraction of the bottle she has drunk altogether.

11.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

12.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

13.Work out 5 + 3 × (9 − 6)

14.Write down the reciprocal of 5/8

15.Amelia eats 5/8 of a bar of chocolate and Oliver eats 3/4 of an identical bar. Write both amounts as eighths and write down the greater of the two fractions.