Rounding

Tier: #Foundation #Higher

How to

Rounding means replacing a number with a nearby value that is simpler to use. You can round to a number of decimal places (d.p.) or significant figures (s.f.).

Decimal places: count digits after the decimal point. $$3.7482 \text{ to 2 d.p.} = 3.75 \quad (\text{the third decimal is 8, so round up})$$

Significant figures: count from the first non-zero digit. $$0.004823 \text{ to 2 s.f.} = 0.0048 \quad (\text{first two sig figs are 4 and 8})$$

Rule: if the digit after your rounding point is 5 or more, round up; if less than 5, round down.

Nearest 10, 100, etc.: same principle applied to whole numbers. $$473 \text{ to the nearest 10} = 470, \quad \text{to the nearest 100} = 500$$

Common error: treating zeros after a rounded digit as insignificant — $3.50$ and $3.5$ are the same value but $3.50$ signals 2 d.p. precision.

Questions to practise

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📝Past paper questions

2025 Jun 3H GCSE Q10 (1 mark)

2024 Nov 2H GCSE Q12 (1 mark)

2024 Jun 3H GCSE Q4 (1 mark)

2023 Nov 2H GCSE Q7 (1 mark)

2023 Jun 2H GCSE Q12 (1 mark)

2023 Jun 2H GCSE Q13 (1 mark)

2023 Jun 3H GCSE Q2 (2 marks)

2022 Jun 2H GCSE Q4 (1 mark)

2022 Nov 2H GCSE Q4 (1 mark)

2022 Jun 2H GCSE Q8 (1 mark)

2022 Nov 2H GCSE Q23 (1 mark)

2022 Jun 3H GCSE Q16 (1 mark)

2022 Nov 3H GCSE Q25 (1 mark)

2021 Nov 1H GCSE Q10 (1 mark)

2021 Nov 2H GCSE Q5 (1 mark)

2021 Nov 3H GCSE Q4 (1 mark)

2021 Nov 3H GCSE Q7 (1 mark)

2020 Nov 3H GCSE Q9 (1 mark)

2020 Nov 3H GCSE Q18 (1 mark)

2019 Jun 2H GCSE Q5 (1 mark)

2019 Jun 2H GCSE Q12 (1 mark)

2019 Nov 2H GCSE Q12 (1 mark)

2019 Nov 2H GCSE Q13 (1 mark)

2019 Nov 2H GCSE Q19 (1 mark)

2019 Nov 3H GCSE Q2 (1 mark)

2019 Nov 3H GCSE Q4 (1 mark)

2019 Jun 3H GCSE Q7 (1 mark)

2019 Jun 3H GCSE Q13 (1 mark)

2019 Nov 3H GCSE Q13 (1 mark)

2019 Nov 3H GCSE Q18 (1 mark)

2019 Jun 3H GCSE Q19 (1 mark)

2019 Jun 3H GCSE Q23 (1 mark)

2019 Nov 3H GCSE Q23 (1 mark)

2018 Nov 2H GCSE Q7 (1 mark)

2018 Jun 2H GCSE Q19 (1 mark)

2018 Jun 2H GCSE Q21 (1 mark)

2018 Nov 3H GCSE Q1 (1 mark)

2018 Nov 3H GCSE Q6 (1 mark)

2018 Jun 3H GCSE Q13 (1 mark)

2018 Jun 3H GCSE Q17 (1 mark)

2017 Nov 2H GCSE Q2 (1 mark)

2017 Nov 2H GCSE Q7 (1 mark)

2017 Nov 2H GCSE Q8 (1 mark)

2017 Nov 2H GCSE Q11 (1 mark)

2017 Nov 2H GCSE Q13 (1 mark)

2017 Nov 2H GCSE Q20 (1 mark)

2017 Jun 2H GCSE Q21 (1 mark)

2017 Nov 3H GCSE Q3 (1 mark)

2017 Jun 3H GCSE Q6 (1 mark)

2017 Jun 3H GCSE Q15 (1 mark)

2017 Nov 3H GCSE Q17 (1 mark)

2017 Jun 3H GCSE Q18 (1 mark)

💬What the examiners say
  • "Students are therefore advised to write down their full calculator display before rounding."
  • "Keep full precision in intermediate calculations."
⬆️How you can quickly improve
  • Write out your full calculator display in the working space before rounding, and count significant figures starting from the first non-zero digit.
  • Never round intermediate values — keep full precision on your calculator right up to the last step.
  • Before rounding to estimate, ask whether your rounded values will actually lead to a calculation you can do mentally — for square roots, look for a nearby perfect square rather than blindly applying one significant figure.
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