Number worksheet — GCSE Foundation

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

2.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

3.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.

4.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

5.Amelia has 49 boxes of apples with 21 apples in each box. Work out an estimate for the total number of apples, by rounding each number to 1 significant figure.

6.A lift has a safe working load of 500 kg. Four people get in the lift and the lift's display records their total mass as 493 kg, correct to the nearest kg. Decide whether the four people are definitely within the safe working load.

7.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

8.Work out the value of 2⁻⁴

9.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

10.Work out an estimate for 312 × 19, by rounding each number to 1 significant figure.

11.A jar of jam costs £2.35. Tom buys 3 jars. He says the total cost is more than £7. Work out the exact total cost, and state whether Tom's claim is correct.

12.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.

13.Last year a company made a profit of £5,200,000. Write this amount in standard form.

14.Work out −7 − (−3).

15.Work out the reciprocal of (2 + 3)