Rounding, Estimation and Accuracy
Rounding affects every question on the paper, because almost every answer has to be given to a stated accuracy. Marks are lost here not through difficulty but through not reading the instruction — or confusing decimal places with significant figures.
1. The rounding rule
Look at the next digit after the place you’re rounding to. 5 or more → round UP. 4 or less → round DOWN (leave it as it is).
- 5.27 to 1 d.p. → next digit is 7 → 5.3
- 5.23 to 1 d.p. → next digit is 3 → 5.2
- 5.3978 to 2 d.p. → next digit is 7 → 5.40
Look only at the ONE digit after the cut-off — not at everything that follows. For 5.2491 to 1 d.p., the deciding digit is 4, so the answer is 5.2, even though 91 follows.
Keep the trailing zero. 5.3978 to 2 d.p. is 5.40, not 5.4 — the zero shows the required accuracy.
2. Decimal places
Count the digits AFTER the decimal point.
| Number | 1 d.p. | 2 d.p. |
|---|---|---|
| 3.2571 | 3.3 | 3.26 |
| 0.0847 | 0.1 | 0.08 |
| 631.94 | 631.9 | 631.94 |
631.9 is 631.94 to 1 d.p., not 631. Rounding to a whole number when 1 decimal place was asked for was a specific recorded error — read what the question wants.
3. Significant figures
Significant figures start from the FIRST NON-ZERO digit, counting from the left.
| Number | 1 s.f. | 2 s.f. | 3 s.f. |
|---|---|---|---|
| 4728 | 5000 | 4700 | 4730 |
| 0.004681 | 0.005 | 0.0047 | 0.00468 |
| 30.62 | 30 | 31 | 30.6 |
Which zeros count?
- Leading zeros never count: in 0.00468 the first significant figure is the 4
- Zeros between digits do count: in 3.05 there are 3 significant figures
- Trailing zeros in a whole number are placeholders: 4700 to 2 s.f. keeps the zeros to preserve the size
You must keep the place-value zeros. 4728 to 2 s.f. is 4700, not 47. Dropping them changes the number by a factor of 100.
In a number with no decimal point, find the first non-zero digit from the LEFT — a difficulty specifically recorded in lessons.
The difference in one line: decimal places count from the decimal point; significant figures count from the first non-zero digit. For 0.00468 those give completely different answers, which is why confusing them is so costly.
4. Estimation
To estimate, round every number to 1 SIGNIFICANT FIGURE, then calculate.
Example: estimate (38.2 × 5.9) ÷ 2.1
- ≈ (40 × 6) ÷ 2
- = 240 ÷ 2 = 120
Example: estimate √(4.2² + 8.9²)
- ≈ √(16 + 81) = √97 ≈ 10
1 significant figure is the standard for estimation — this is the convention examiners expect. Advice given in one lesson to round “to the nearest whole number” is not the rule: for a number like 38.2 that would give 38, which defeats the purpose of an estimate you can do in your head.
An estimate is not an exact answer. You are meant to lose accuracy — a student who worked out the exact value had misunderstood the question. Show the rounded values in your working, because that is where the marks are.
Estimating square roots: find the square numbers either side. √50 lies between √49 = 7 and √64 = 8, so it is just over 7.
Why estimate? To check a calculator answer is sensible. If your estimate is 120 and the calculator says 1.2, you have mistyped something.
5. Accuracy in your answers
Give 3 significant figures unless the question says otherwise. This is the general rule for non-exact answers.
Exceptions:
| Context | Accuracy |
|---|---|
| Money | 2 decimal places |
| Angles | often 1 decimal place |
| The question specifies | follow the question |
| Exact answers (surds, π, fractions) | leave them exact |
Do not round intermediate values. Carry the full figure through multi-step calculations and round only the final answer. Rounding at each stage accumulates errors large enough to lose accuracy marks — and this was flagged in nearly every topic.
A question asking for a specific accuracy is telling you something. “Give your answer to 2 decimal places” usually means the answer is not exact — so don’t hunt for a whole number.
Writing large numbers: if a question asks for a value in figures, write 25 000 000, not “25M” or “25 million” — a documented error.
6. Mistakes that cost marks
Confusing decimal places with significant figures.
Rounding to a whole number when decimal places were asked for.
Looking at more than one digit past the cut-off.
Dropping trailing zeros that show accuracy.
Dropping place-value zeros in significant-figure rounding.
Counting leading zeros as significant.
Rounding to the wrong number of figures in an estimate.
Giving an exact answer when an estimate was asked for.
Not showing the rounded values in estimation working.
Rounding intermediate steps.
Ignoring the accuracy stated in the question.
Using abbreviations like “25M” instead of figures.
Frequently asked questions
What is the rounding rule? Look at the next digit: 5 or more rounds up, 4 or less stays.
What is the difference between decimal places and significant figures? Decimal places count from the decimal point; significant figures count from the first non-zero digit.
How do I round 0.004681 to 2 significant figures? The first significant figure is the 4, so the answer is 0.0047.
Do zeros count as significant figures? Leading zeros don’t; zeros between digits do.
What is 4728 to 2 significant figures? 4700 — the zeros hold the place value.
How do I estimate a calculation? Round every number to 1 significant figure, then calculate.
Why is my estimate not exactly right? Because it is an estimate — that is the point. It checks whether your exact answer is sensible.
What accuracy should I use? 3 significant figures unless told otherwise — but 2 decimal places for money.
Should I round in the middle of a calculation? No — carry full accuracy and round only at the end.
Quick revision checklist
- I know the 5-or-more rounding rule
- I look at only one digit past the cut-off
- I can round to a given number of decimal places
- I keep trailing zeros where they show accuracy
- I can round to significant figures, starting at the first non-zero digit
- I keep place-value zeros
- I know which zeros are significant
- I can tell d.p. from s.f. instantly
- I estimate by rounding to 1 significant figure
- I show my rounded values in estimation working
- I give 3 s.f. by default and 2 d.p. for money
- I never round intermediate values
- I read the accuracy the question asks for
These notes cover rounding, estimation and limits of accuracy in the Cambridge IGCSE Mathematics (0580) syllabus, and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Maths lessons, with particular attention to the errors students make most often and the wording examiners reward. Always check the current syllabus for your own exam series.
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