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IB Chemistry: Uncertainties & Significant Figures — FAQ
Answered by RevisionPrep's IB Educators
Uncertainty and significant figure errors cost more marks than any other habit I see marking IB Chemistry papers and IAs. Get the rules straight once and they stop being a mystery. Here's how to answer these questions properly, at SL and HL.
Understanding the concept
How do you answer uncertainties & significant figures questions in IB Chemistry?
Check the precision of your equipment first, then round your final answer to match your least precise measurement — usually the one with the fewest significant figures. Quote absolute uncertainty on raw readings and percentage uncertainty once you've propagated through a calculation. Examiners mark both the number and its stated uncertainty.
Quick tip: if a burette reads to ±0.05 cm³ and a balance reads to ±0.001 g, your titre volume — not the mass — usually limits your final sig figs, because it typically has the largest relative uncertainty.
What is the correct number of significant figures in IB Chemistry calculations?
Your final answer should carry the same number of significant figures as the least precise piece of raw data used to calculate it — not more, not fewer. If a concentration is measured to 3 sig figs and a volume to 4, your final answer is rounded to 3.
Worked example: mass = 1.20 g (3 sf), volume = 25.00 cm³ (4 sf). Concentration = mass ÷ volume gives 0.0480 g cm⁻³ — rounded to 3 sig figs, matching the mass, the weaker link.
What's the difference between uncertainty and error in IB Chemistry?
Error is the difference between a measured value and the true or accepted value — it tells you how wrong a result is. Uncertainty is the range within which the true value probably lies, based on the limits of your equipment. You calculate uncertainty before you ever compare to a literature value.
Systematic error (a consistently high or low reading, like a badly calibrated pH meter) shifts every result the same way and won't show up as scatter. Random error causes the scatter that repeat trials and standard deviation reveal — uncertainty is your estimate of that scatter's size.
How to calculate and propagate uncertainty
How do you calculate percentage uncertainty in IB Chemistry?
Percentage uncertainty equals the absolute uncertainty divided by the measured value, multiplied by 100. For a burette reading of 24.50 cm³ with an uncertainty of ±0.05 cm³, that's (0.05 ÷ 24.50) × 100, giving 0.20%. Smaller measured volumes always produce larger percentage uncertainties for the same equipment.
This is why chemists prefer larger titres where possible — a 5 cm³ titre with a ±0.05 cm³ burette uncertainty gives a 1% error, ten times worse than a 25 cm³ titre with the same absolute uncertainty.
How do you propagate uncertainty when adding/subtracting or multiplying/dividing?
For addition or subtraction, add the absolute uncertainties of each value together. For multiplication or division, add the percentage uncertainties of each value together, then convert back to an absolute uncertainty on the final answer if needed. Never mix absolute and percentage uncertainties in the same step.
Worked example: titre = final reading (24.50 ± 0.05) − initial reading (0.20 ± 0.05) = 24.30 cm³, with absolute uncertainty ±0.10 cm³ (0.05 + 0.05). If this titre is then used in c = n ÷ V, convert 0.10 cm³ to a percentage uncertainty (0.10 ÷ 24.30 × 100 ≈ 0.41%) before adding it to the percentage uncertainty on n.
How many sig figs should you use for a titration result?
Your titre volume is normally quoted to 2 decimal places (matching a burette's ±0.05 cm³ precision), and your final calculated concentration is rounded to the same number of significant figures as the least precise measurement feeding into it — usually 3 sig figs for typical school-lab data.
Common mistake: students copy a calculator's 8-digit output straight into their answer. If your mass balance only reads to 3 sig figs, reporting 0.048372 mol dm⁻³ instead of 0.0484 mol dm⁻³ loses marks under IA criterion 'Data Analysis', even if the arithmetic is correct.
Exam & syllabus specifics
Why do IB Chemistry exams penalise wrong significant figures?
Because a numerical answer with too many sig figs claims a precision your data doesn't support — it's treated as a conceptual error, not a rounding slip. Markschemes typically allow one mark for the correct method and a separate mark for correct sig figs, so getting the maths right isn't enough on its own.
Markschemes usually accept an answer to ±1 in the last significant figure, but they'll still deduct a mark if you report, say, five sig figs from data that only supports three.
Do significant figures matter in IB Chemistry Paper 1 and Paper 2?
Yes, though differently. Paper 1 (multiple choice) rarely tests sig figs directly since answers are pre-set options, but Paper 2's calculation questions award specific marks for reporting your final answer to an appropriate number of significant figures — usually stated in the markscheme as a separate marking point.
In Paper 2 long-answer questions, examiners are told to accept a range of final answers if the working is correct, but the sig-fig mark stands alone — get the chemistry right and still drop a mark for writing four sig figs when the data supports two.
How do uncertainties apply to the Internal Assessment (IA)?
Uncertainty treatment is assessed explicitly under the Data Analysis criterion of the scientific investigation. According to the IB, the current DP Sciences guide (first assessment 2025) marks the IA out of 24 across four criteria — Research Design, Data Analysis, Conclusion, Evaluation — and top marks require propagated uncertainty, not just raw instrument uncertainty on a table.
3 things examiners check in Data Analysis:
- Raw uncertainties recorded in every data table header (e.g. ±0.05 cm³).
- Uncertainty correctly propagated through calculations to the final processed result.
- That final uncertainty used sensibly in the Evaluation to judge whether a conclusion is actually supported.
Comparisons & getting extra help
Is IB Chemistry HL harder than SL for uncertainty calculations?
The underlying rules are identical at SL and HL — same propagation methods, same sig-fig conventions. HL students meet uncertainty in more complex multi-step calculations (equilibrium constants, kinetics rate data), so mistakes compound across more steps, but no extra uncertainty content is unique to HL.
| Aspect | SL | HL |
|---|---|---|
| Uncertainty rules taught | Same | Same |
| Typical calculation length | 1-2 steps | 3-5 steps |
| IA expectations | Same 4 criteria, /24 | Same 4 criteria, /24 |
| Where marks are lost | Final rounding | Propagation partway through |
How can parents help their child improve at uncertainty/sig fig questions?
The biggest gain comes from repetition of past-paper calculation questions with the markscheme open, not re-explaining the theory. Ask your child to talk through why they rounded to a particular number of sig figs — if they can't explain it, they're guessing rather than applying the rule, and that's an easy, fixable habit.
It's also worth checking whether your child's school covers uncertainty propagation early enough — some schools leave it until the IA is due, which is too late to build the habit for exam calculation questions.
What resources help you practice uncertainties and significant figures?
Past paper Section A and B calculation questions are the best practice, since markschemes show exactly where the sig-fig mark sits. On RevisionPrep, the Chemistry Topical Worksheets isolate uncertainty and data-processing questions by topic, and the Revision Notes summarise the propagation rules in one place for quick reference before a mock.
Checklist before your next mock:
- Can you state the rule for addition/subtraction vs multiplication/division uncertainty?
- Do you round your final answer to match your least precise raw measurement?
- Have you practised converting absolute to percentage uncertainty and back?
- Do you know which IA criterion assesses this?
IB Chemistry SL vs HL: Uncertainty & Sig Fig Expectations
| Aspect | SL | HL |
| Uncertainty rules taught | Same rules | Same rules |
| Typical calculation length | 1-2 steps | 3-5 steps |
| IA criteria used | 4 criteria, /24 | 4 criteria, /24 |
| Common mark loss | Final rounding | Mid-calculation propagation |
For more worked calculation practice, check the Chemistry Topical Worksheets and Revision Notes on RevisionPrep, covering uncertainty propagation and IA data analysis in detail.