Mathematics 0580 · syllabus C1.9, E1.9
Cambridge IGCSE Mathematics 0580 — Rounding and estimation topical past papers
Rounding to decimal places and significant figures, estimating a calculation by rounding each number to 1 significant figure, and choosing a sensible accuracy.
- Questions
- 51
- Years
- 2010–2026
- With mark scheme
- 100%
- Questions 2022–2026
- 39
Anyone can browse these pages. Opening the questions and their mark schemes takes a free Momentum account.
What Rounding and estimation covers
Rounding gives a value to a stated accuracy: to the nearest 10 or 1000, to a number of decimal places, or to a number of significant figures, where the first significant figure is the first digit that is not zero. So 0.040 76 is 0.0408 to 3 significant figures, and 18 649 is 19 000 to 2 significant figures; the zeros in 19 000 hold place value and must stay.
Estimation means rounding each number in a calculation, usually to 1 significant figure, and working out the simpler calculation by hand: 28.7 × 0.49 ÷ 6.12 is roughly 30 × 0.5 ÷ 6 = 2.5. The other skill is choosing a sensible accuracy for an answer in context, such as a whole number of buses or a length to the nearest centimetre.
Rounding and estimation are Core content, so they can be set on all four papers. On the calculator papers, inexact answers are expected to 3 significant figures, and angles in degrees to 1 decimal place, unless a question sets its own accuracy; keeping full values until the final answer protects the accuracy marks. On the non-calculator papers an estimate is the quickest check of any calculation, and upper and lower bounds follow on directly from rounding.
In the syllabus
The headings this topic has in the Cambridge International 2025–2027 syllabus, as the board prints them.
- C1.9 Estimation
- E1.9 Estimation
What you should be able to do
- Round to the nearest 10, 100 or 1000, to a given number of decimal places, or to significant figures
- Find the first significant figure of a number smaller than 1
- Estimate a calculation by rounding each value to 1 significant figure, showing the rounded values
- Round an answer to an accuracy that suits its context, such as a whole number of items
- Use an estimate to check whether a calculator answer is reasonable
Key ideas
- Significant figures count from the first non-zero digit, and zeros between non-zero digits are significant
- Look at the next digit: 5 or more rounds up, 4 or less leaves the digit as it is
- Rounding keeps the size of a number, so place-holding zeros stay: 7350 to 1 significant figure is 7000
- An estimate rounds every value before calculating; it does not round the exact answer afterwards
How Rounding and estimation has been examined
From 2022 to 2026, Rounding and estimation was on Paper 1 · Non-calculator (Core) in 12 of 14 exam series, worth about 2% of that paper’s marks.
| Paper | Questions | Share of marks | Series |
|---|---|---|---|
| Paper 1 · Non-calculator (Core) | 24 | 2% | 12 of 14 |
| Paper 2 · Non-calculator (Extended) | 4 | 1% | 4 of 14 |
| Paper 3 · Calculator (Core) | 7 | 1% | 5 of 14 |
| Paper 4 · Calculator (Extended) | 4 | 1% | 4 of 14 |
Momentum’s own count, over the questions in its bank for these years: a series is one exam session, every zone included, and a question filed under two chapters counts in both. Median marks per question: 2.
Filed in Momentum under: Approximation and Estimation.
A worked example
Estimate (61.8 × 0.293) ÷ (3.87 + 1.94) by rounding every number in it to 1 significant figure.
- Round each number to 1 significant figure: 61.8 ≈ 60, 0.293 ≈ 0.3, 3.87 ≈ 4 and 1.94 ≈ 2.
- Write the rounded calculation: (60 × 0.3) ÷ (4 + 2).
- Top: 60 × 0.3 = 18. Bottom: 4 + 2 = 6.
- Estimate: 18 ÷ 6 = 3. A calculator gives 3.12 to 3 significant figures, so the estimate is reasonable.
Answer: About 3
Written by Momentum for this page, with its own numbers; it is not taken from a past paper.
Mistakes that cost marks
- Dropping place-value zeros: 38 270 to 2 significant figures is 38 000, not 38, because the answer must still be about thirty-eight thousand.
- Starting the count of significant figures at a leading zero: in 0.0629 the first significant figure is 6, so to 2 significant figures it is 0.063.
- Working out the exact answer and rounding it when an estimate is asked for: the method mark is for showing each number rounded, usually to 1 significant figure, before calculating.
- Rounding values part of the way through a calculation on the calculator papers: an answer built from rounded steps can miss the 3 significant figure accuracy mark.
- Giving an answer that does not fit its context, such as 13.4 buses: a number of buses must be whole, and rounded up if everyone needs a seat.
Exam technique
- Underline the digit you are rounding to and look only at the digit after it.
- In an estimate, write the rounded calculation in full, such as 30 × 0.5 ÷ 6, before simplifying, and round a number like 0.49 to 0.5, not to 0.
- On the calculator papers, write down more figures than you need from the display, then round the final answer to 3 significant figures.
Practising in Momentum
- Every question in a chapter as one list, from every paper and year in the bank, newest first or shuffled.
- Each question turns over to its own part of the mark scheme, where the board published one.
- Narrow by paper, year, session, zone and marks, and star the questions worth keeping.
- Pick chapters, a number of questions and a time, and the exam builder draws a mock to sit and mark.
Past-paper questions and mark schemes are the copyright of Cambridge International. Momentum shows them to signed-in learners for revision and does not publish them on these pages.