Number worksheet — GCSE Higher

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

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

3.Work out 36 ÷ (2 × 3)

4.Work out ((−3) + 5) × (−4) − (−6) ÷ 2

5.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

6.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20

7.Write 12 as a product of its prime factors.

8.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

9.Write 5/6 as a decimal, showing clearly which digit recurs.

10.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.

11.Work out (−36) ÷ (−6) × 2

12.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

13.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.

14.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.

15.Work out 5/6 × 2/9, giving your answer in its simplest form.