Number worksheet — GCSE Higher

1.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.

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

3.Work out the value of √49 + ∛27

4.Write these numbers in order, starting with the smallest: −1.4, 5/4, −6/5, 1.3, 0

5.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.

6.Find the missing number: 17 × ▢ = 391

7.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

8.Work out (−2)² − 3

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

10.Work out 6² − 4².

11.Estimate the value of √45, giving your answer to the nearest whole number.

12.A bag of flour is labelled 1.5 kg, correct to the nearest 0.1 kg. The true mass of the flour is m kg. Which inequality gives all the possible values of m?

13.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

14.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.

15.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.