Number worksheet — GCSE Higher

1.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.

2.A flight departs at 21:35 and lands at 06:10 the following morning. Work out the total flight time.

3.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

4.Simplify ⁴√(16a⁸b¹²)

5.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.

6.A charity raises 8 × 10⁶ pounds. This total is shared equally among 2 × 10² local projects. Work out how much each project receives, in standard form.

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

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

9.Meera says that 0.7 ÷ 0.1 = 0.07. Work out the correct value of 0.7 ÷ 0.1.

10.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

11.Work out 5⁰ + 5¹ + 5²

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

13.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

14.Work out √144 − 2 × 3 + √25

15.2/3 of an amount of money is £30. Work out the amount.