Number worksheet — GCSE Higher

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

2.A weather app records the temperature at three points in one day: 6 °C at noon, −2 °C at midnight, and −7 °C just before dawn. Work out the difference between the highest and lowest of these three temperatures.

3.2/3 of an amount of money is £30. Work out the amount.

4.Sam compares 0.6 and 5/8 by comparing the digit 6 with the digit 5, and says that 0.6 is the larger number. Convert 5/8 to a decimal to find the correct larger value.

5.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.

6.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

7.Write 7/12 as a decimal, showing clearly which digit is recurring.

8.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

9.Round 0.006852 to 2 significant figures.

10.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

11.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

12.Work out the value of √(16 + 9)

13.Write ∛(x²) as a single power of x.

14.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

15.Write 200 as a product of its prime factors, using index notation.