Rounding and Significant Figures (AI SL)
IB questions expect you to round correctly to either decimal places or significant figures, and to know these are different rules that can give different answers to the same number. This page covers both conventions, how to choose a sensible degree of accuracy, and the trap of rounding too early - with worked examples and the mistakes that lose the most marks. It's part of the broader Approximation & Error topic.
18 questions on this sub-topic.
Significant figures
Covered under IB syllabus reference SL1.6: approximation - decimal places and significant figures. Students should be able to choose an appropriate degree of accuracy based on given data.
Significant figures (s.f.)
Start counting from the first non-zero digit, in either direction from the decimal point.
\(48\,372\) to 2 s.f. \(= 48\,000\) - only the 4 and 8 are kept as meaningful digits.
Not in the formula booklet - prior knowledgeDecimal places (d.p.)
Count digits after the decimal point, regardless of where the number's meaningful digits start.
\(0.040719\) to 2 d.p. is \(0.04\), but to 2 s.f. it's \(0.041\) - the two rules genuinely disagree here, so always check which one the question asks for.
Need the full syllabus wording and formula-booklet reference table? See Approximation & Error. For GDC display settings, see the parent topic's GDC guidance.
Worked examples
Round \(47.3856\) to
(a) 2 decimal places.
(b) 1 decimal place.
Worked solution
(a) \(47.3856\): the 3rd decimal is \(5\), so the 2nd decimal \(8\) rounds up to \(9\) \(\Rightarrow 47.39.\) A1
(b) \(47.3856\): the 2nd decimal is \(8\ (\ge5)\), so the 1st decimal \(3\) rounds up to \(4\) \(\Rightarrow 47.4.\) A1
A circle has radius 6.3 cm.
(a) Find its area, giving the full calculator value.
(b) Round your answer to 3 significant figures.
Worked solution
(a) Step 1 - Apply \(A=\pi r^2\) with \(r=6.3\): \(A = \pi(6.3)^2 = \pi(39.69)\) M1
\(= 124.689\ldots\) cm² (keep the full display). A1
(b) To 3 significant figures the first three figures are \(1,2,4\); the next digit is \(6\ (\ge5)\), so round up \(\Rightarrow A\) A1
\(\approx 125\) cm². A1
Common mistakes
- Counting leading zeros as significant figures. In \(0.003080\), the three zeros before the \(3\) are not significant - only \(3,0,8,0\) count, giving 4 s.f., not 7.
- Mixing up decimal places and significant figures. Decimal places count from the decimal point; significant figures count from the first non-zero digit. \(0.004567\) is \(0.00\) to 2 d.p. but \(0.0046\) to 2 s.f.
- Rounding intermediate values before the final step. Rounding too early compounds error through a calculation. Keep full calculator precision throughout, and round only the final answer.
Ready to practise properly?
22 rounding and significant-figures questions, marked instantly like the real exam.
Quick answers
How do you round to a given number of significant figures?
Count significant figures starting from the first non-zero digit. Keep that many digits, look at the next digit to decide whether to round up, and fill any remaining places before the decimal point with zeros.
Are leading zeros significant?
No. In \(0.003080\), the zeros before the \(3\) are not significant - only \(3, 0, 8, 0\) count, giving 4 significant figures.