Significant figures, units and reporting the result
Why this page exists
- The Excellence criterion says the concentration must be determined "including correct use of significant figures and units".
- This is one of the few places in NCEA Chemistry where presentation is explicitly a graded criterion rather than good practice. An otherwise perfect investigation reported to the wrong precision cannot reach Excellence.
How many significant figures
- The answer carries the same number of significant figures as the least precise measurement that went into it.
- Work out which measurement that is before you round.
| Measurement | Typical precision | Significant figures |
|---|---|---|
| Mass on a 4-figure balance, 2.6738 g | ±0.0001 g | 5 |
| Burette titre, 17.90 mL | ±0.05 mL | 4 |
| Pipette aliquot, 20.0 mL | ±0.06 mL | 3 |
| Volumetric flask, 250.0 mL | ±0.2 mL | 4 |
| Concentration of standard, 0.1009 mol L−1 | — | 4 |
- In a typical titration the limiting measurement is the pipette aliquot at 3 significant figures, so 3 sf is the usual answer.
- Exact numbers do not limit precision. A dilution factor of 10, or the 2 in a 2 : 1 mole ratio, is exact — it has infinite significant figures.
The units that go with each quantity
| Quantity | Unit | Written as |
|---|---|---|
| Amount of substance | mole | mol |
| Concentration | moles per litre | mol L−1 |
| Mass concentration | grams per litre | g L−1 |
| Molar mass | grams per mole | g mol−1 |
| Volume | litres or millilitres | L, mL |
| Mass | grams | g |
- Write units with a negative index: mol L−1, not mol/L. Both are understood, but the index form is the convention used in NCEA Chemistry and "conventions" is named in the criteria.
- Every number in your working carries a unit, not just the final answer.
Rounding rules
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Round once, at the end. Carry unrounded values through every intermediate step.
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Show intermediate values with "..." to make clear you carried more digits: mol.
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Round the final value only, and state its unit.
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Rounding at each step is visible: a marker redoing your arithmetic will get a slightly different answer and will know why.
Reporting the result for a consumer product
- Give the answer in the units the product uses, as well as in mol L−1.
- Vinegar is sold by % acidity.
- Vitamin C tablets are labelled in mg per tablet.
- Bleach is labelled by % available chlorine.
- Then compare with the label — that comparison is the beginning of the Excellence evaluation.
Evaluating the outcome in relation to the product
The Excellence criterion asks you to evaluate the outcome in relation to the consumer product. That means answering questions like:
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Does the result match the label? By how much does it differ?
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Is the difference within the manufacturing tolerance, or too large to be explained that way?
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Could the difference be explained by the product itself — decomposition with age, settling, evaporation, a "minimum content" claim rather than an exact one?
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Does the result have a practical consequence — is the antacid effective, is the vitamin C tablet worth its price, is the bleach still strong enough to disinfect?
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A conclusion that stops at the number has not evaluated anything. The evaluation is what the number means for the product.
Worked ExampleReporting and evaluating a result
A student determines the ethanoic acid content of a vinegar as 0.824857... mol L−1, from a 20.0 mL pipetted aliquot, a mean titre of 16.35 mL, and a standard solution of 0.1009 mol L−1. The bottle is labelled "acidity 4%". Report the result correctly and evaluate it in relation to the product. (M(CH3COOH) = 60.05 g mol−1)
Step 1 — Decide the significant figures
The measurements were:
- Titre 16.35 mL — 4 sf
- Standard solution 0.1009 mol L−1 — 4 sf
- Aliquot 20.0 mL — 3 sf
The dilution factor of 10 is exact and does not limit anything.
The least precise is the aliquot at 3 sf, so the answer is reported to 3 significant figures.
Step 2 — Convert to the product's own units
For a dilute aqueous solution, 1 L has a mass of approximately 1000 g, so:
Step 3 — Compare with the label
The label claims 4%; the measured value is 4.95%, about 24% higher in relative terms.
Step 4 — Evaluate
- Is the difference explicable by the product? Vinegar labels in New Zealand generally state a minimum acidity, and food-grade vinegars are commonly produced at 5% or above. A measured 4.95% against a stated 4% is entirely consistent with a product comfortably meeting a minimum claim, rather than with an error.
- Is it explicable by error? A 24% discrepancy is far too large for burette reading error (about 0.6%) or endpoint judgement. It would require a substantial systematic error, and the two candidates — an unstandardised titrant or a misapplied dilution factor — would produce errors of a few percent and of a factor of ten respectively. Neither matches 24%.
- What it means practically: the vinegar is stronger than its label suggests, so it is fit for purpose for both culinary and preserving use, where a minimum acidity of 4% is what matters for inhibiting microbial growth.
Answer: 0.825 mol L−1, equivalent to 49.5 g L−1 or 4.95% by mass. This exceeds the stated 4% acidity, which is consistent with the label being a minimum guaranteed value rather than an exact one — the product meets and exceeds its claim.