Why Did My IB Teacher Mark My Sig Figs Wrong? Common IA Deductions Explained

Rule Statement: What IB Actually Expects

IB does not award a separate ‘significant figures’ mark, yet sig figs affect several internal assessment criteria. In the IB DP sciences, data collection and processing, conclusion, and communication criteria expect precision to be consistent with the measurements you actually made. A teacher may deduct when a final result implies more precision than the instrument, method, or raw data can support. This site is a precision-and-rounding reference, not just a calculator: the Significant Figures rule pages and Rounding Rules explain the conventions behind the answer.

For IB IA work, the working expectations are:

• Multiplication and division: the result carries the same number of significant figures as the least precise measured factor.
• Addition and subtraction: the result is limited by the least precise decimal place, not by the count of significant figures.
• Uncertainty: report uncertainty to one or two significant figures, and round the measured value to the same decimal place.
• Exact numbers: counts, definitions, stoichiometric coefficients, and defined conversion factors do not limit precision.
• Consistency: table columns, calculated values, graphs, and conclusions should show a coherent precision story.

The numerical values of the estimate and its standard uncertainty should not be given with an excessive number of digits. – JCGM 100:2008 (GUM), Clause 7.2.6

Convention Comparison Table

IB expectations align broadly with international metrology practice, but teachers may apply rubric language more strictly. Use this table to compare common contexts.

Standards Citation: Where the Rules Come From

Specific standards make precision rules defensible. The IB rubric is the immediate authority for your IA, but these documents explain the underlying conventions:

• ISO 80000-1:2009, Quantities and units – Part 1: General, Clause 7.3.3 covers rounding and significant digits in quantity values.
• ASTM E29-13(2019), Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications, Sections 4-7, gives practical rounding and conformance rules.
• JCGM 100:2008 (GUM), Clause 7.2.6, states that measurement results and uncertainties should not be reported with excessive digits.
• NIST Technical Note 1297, Appendix A, gives NIST guidance for expressing uncertainty, including one- or two-significant-digit uncertainty statements.
• IB DP Sciences Guide, internal assessment criteria for data collection and processing and communication, require appropriate and consistent significant figures.

When your teacher marks you down, the issue is rarely the calculator. It is usually the gap between the raw measurement precision and the reported digits.

Worked Examples: IB IA Calculations

Example 1: Multiplication and Division

A student measures a rectangle as 12.3 cm by 4.56 cm. The raw values have 3 and 3 significant figures. The calculator gives 56.088 cm². The least precise factor has 3 significant figures, so the area is 56.1 cm². Reporting 56.088 is a common IA deduction because it implies precision to thousandths of a square centimetre that the ruler cannot support.

Example 2: Addition and Subtraction

A student adds 12.34 g and 0.1 g. The calculator gives 12.44 g, but 0.1 g is precise only to the tenths place. The result must be rounded to the tenths place: 12.4 g. The significant-figure count of 12.34 is irrelevant here; decimal place controls.

Example 3: Uncertainty

A mean time is 0.1234 s with uncertainty 0.0567 s. If the uncertainty is reported to one significant figure, it becomes 0.06 s, and the value becomes 0.12 s. If reported to two significant figures, it becomes 0.057 s, and the value becomes 0.123 s. Both 0.12 ± 0.06 s and 0.123 ± 0.057 s can be acceptable if used consistently. The error is writing 0.1234 ± 0.0567 s with no rounding.

Example 4: Exact Numbers

Density is mass divided by volume. If mass is 25.0 g and volume is 10.0 cm³, the density is 2.50 g/cm³. A factor of 2 in the formula V = πr²h is exact; it does not reduce the answer to one significant figure. Likewise, 1000 mL/L is exact within the SI system.

Counter-Examples: What Triggers Deductions

These are common moves that look precise but lose marks:

• Calculator worship: reporting 56.088 cm² when inputs have three significant figures.
• Double rounding: rounding an intermediate mean to 2 sig figs, then using that rounded value in a final calculation. See Double Rounding Error.
• Ambiguous trailing zeros: writing 1200 m for a value with three significant figures. Write 1.20 × 10³ m or use an overline. See Ambiguous Trailing Zeros.
• Uncertainty mismatch: reporting 0.1234 ± 0.0567 s instead of rounding uncertainty and value to matching decimal places.
• Exact-number error: treating a stoichiometric coefficient of 2 as having one significant figure and rounding a final molar value incorrectly.
• Wrong operation rule: applying multiplication sig-fig counting to an addition problem such as 10.0 g + 0.123 g.

Common Mistakes

1. Rounding too early. Keep guard digits during calculations and round only at the end.
2. Ignoring decimal places in addition. The limiting factor is the leftmost uncertain decimal place.
3. Reporting every calculator digit. A digital display is not a measurement claim.
4. Mismatching uncertainty and value. The value and its uncertainty should share the same final decimal place.
5. Counting exact numbers as measured. Counts, definitions, and conversion factors are exact.
6. Inconsistent sig figs in tables. A column should not mix 2.1, 2.15, and 2.147 without a reason.
7. Confusing precision with accuracy. Sig figs describe reporting precision, not how close a result is to the true value.
8. Using the wrong rounding rule silently. State or follow your course convention; avoid half-up and half-even mixing in one report.

Discipline Note: Physics, Chemistry, Biology, and Engineering

Physics IA work often uses uncertainty propagation, percentage uncertainty, and logarithmic graphs. In physics, the decimal places in a logarithm relate to significant figures in the original value, and uncertainty should be propagated before final rounding. Chemistry IA work often uses glassware precision, molar masses, and titration volumes; the least precise measurement controls the final concentration or mole value. Biology IA work often reports means, standard deviations, and percent error; descriptive statistics should not be reported with more decimal places than the raw data. Engineering and applied science reports may follow ISO 80000-1, ASTM E29, or GUM more formally, but IB examiners still look for the same core behaviour: appropriate, consistent, and honest precision.

Quick Reference Table

Practice Problems

Try these before checking the reasoning. They mirror typical IB IA deductions.

1. Calculate 3.45 cm × 2.1 cm.
   Answer: 7.2 cm². The factor 2.1 has 2 significant figures.
2. Add 15.00 mL and 0.25 mL.
   Answer: 15.25 mL. Both values are precise to the hundredths place.
3. Report 0.0789 ± 0.00345 m with uncertainty to one significant figure.
   Answer: 0.079 ± 0.003 m. The value is rounded to the thousandths place.
4. Divide 25.0 g by 5.00 g.
   Answer: 5.00. Both measurements have 3 significant figures.
5. Write 1200 with three significant figures in scientific notation.
   Answer: 1.20 × 10³.