Significant Figures in IB Sciences: DP1 Guide

For M28 students, IB examinations take place in May 2028 after beginning DP1 in August 2026.

Significant figures in IB sciences communicate the precision justified by measured data. Your final answer should not suggest greater certainty than the measurements allow. Keep unrounded calculator values during working, then round the final answer appropriately.

This guide explains how to count significant figures, apply calculation rules, report uncertainties, and avoid common mistakes in IB Chemistry and Physics. Exact marking depends on the question and its markscheme, so an explicit rounding instruction always takes priority.

What are significant figures?

Significant figures, or sig figs, are the meaningful digits in a measured or calculated quantity. They begin with the first non-zero digit and indicate how precisely the value is known.

A balance reading of 2.40 g has three significant figures. Its final zero shows that the mass was measured to the nearest 0.01 g, while 2.4 g indicates precision only to the nearest 0.1 g.

Significant figures describe precision, not accuracy. A result may contain several significant figures yet remain inaccurate because of poor calibration, systematic error, or an unsuitable experimental method.

How to count significant figures

Scientific notation removes ambiguity. Write $1.5\times10^3$ for two significant figures, $1.50\times10^3$ for three, and $1.500\times10^3$ for four.

Changing units does not change precision. Both 0.0250 m and 2.50 cm contain three significant figures.

Significant figures in IB calculations

Multiplication and division

For multiplication or division, the final result normally has the same number of significant figures as the measured input with the fewest significant figures.

For example, calculate the amount of substance in $4.25\text{ g}$ of a compound with molar mass $58.44\text{ g mol}^{-1}$:

$$n=\frac{4.25}{58.44}=0.072724\ldots\text{ mol}$$

The mass has three significant figures, so report 0.0727 mol. The four-significant-figure molar mass cannot justify a more precise result because the measured mass is less precise.

Addition and subtraction

For addition or subtraction, compare decimal places, not significant figures:

$$12.46\text{ cm}+3.2\text{ cm}=15.66\text{ cm}$$

Because 3.2 cm is known only to the nearest 0.1 cm, report 15.7 cm. This difference between decimal-place and significant-figure rules is a frequent source of errors.

Mixed calculations

Do not round after every step. Retain the full calculator value or several guard digits, complete the calculation, and round once at the end. Premature rounding can alter the final digit and create an avoidable disagreement with the markscheme.

Sig figs in IB Chemistry

Significant figures appear in stoichiometry, concentrations, gas calculations, energetics, titrations, and experimental analysis. If $n=0.00562\text{ mol}$ and $V=0.250\text{ dm}^3$, then:

$$c=\frac{0.00562}{0.250}=0.02248\text{ mol dm}^{-3}$$

Both inputs have three significant figures, so report 0.0225 mol dm$^{-3}$. The leading zeros only position the decimal point.

Stoichiometric coefficients and exact counts do not limit precision. Measured masses, temperatures, pressures, and volumes usually do. Practise these distinctions with the IB Chemistry Questionbank, IB Chemistry resources, and the measurement and analysis question guide.

Sig figs in IB Physics

IB Physics calculations combine measured distances, times, currents, voltages, masses, and angles. For a distance of $2.36\text{ m}$ and time of $0.84\text{ s}$:

$$v=\frac{2.36}{0.84}=2.8095\ldots\text{ m s}^{-1}$$

The time has two significant figures, so report 2.8 m s$^{-1}$. Writing 2.8095 would imply unsupported precision.

For graph gradients, choose points far apart on the best-fit line, calculate using suitable precision, and include gradient units. The IB Question Bank for Group 4 sciences provides practice within complete exam-style problems rather than isolated rounding exercises.

Significant figures and uncertainties

Significant figures and uncertainty are related but different. Significant figures control how a value is displayed, while uncertainty estimates the interval within which the value is expected to lie.

A common convention is to state an absolute uncertainty to one significant figure, or occasionally two when justified, then round the measured value to the same decimal place:

$$L=(12.4\pm0.2)\text{ cm}$$

Writing $(12.437\pm0.2)\text{ cm}$ is inconsistent because the measured value claims precision beyond the uncertainty. Percentage uncertainty is calculated as:

$$\text{percentage uncertainty}=\frac{\text{absolute uncertainty}}{\text{measured value}}\times100\%$$

For $(12.4\pm0.2)\text{ cm}$, the percentage uncertainty is approximately 1.6%. Follow any conventions specified by the question or your course rather than treating one classroom shortcut as a universal IB rule.

Instrument readings, data tables, and constants

Precision begins before you press any calculator key. Record an analogue scale only as precisely as its smallest divisions reasonably permit, and record every digit shown by a digital instrument. A digital display of 7.30 V should normally remain 7.30 V, because rewriting it as 7.3 V discards information about resolution.

When a question provides values in a data booklet or table, do not automatically assume that every printed digit is a measured limitation. Physical constants may be given to more figures than needed so they do not control the answer's precision. By contrast, a measured value copied from an experiment usually does limit the result.

For logarithmic quantities such as pH, or results produced from graph fitting, simple classroom shortcuts may not capture the full convention. Use the precision implied by the question, data, and markscheme, and state assumptions if the situation is genuinely ambiguous. Clear working can show that your method is scientifically consistent even when a final rounding choice is debatable.

Common mistakes and an exam method

Avoid these recurring errors:

• Counting leading zeros as significant
• Removing meaningful trailing zeros
• Applying the multiplication rule to addition
• Rounding every intermediate result
• Omitting units
• Assuming every answer requires three significant figures
• Confusing significant figures with decimal places

The value 0.00450, for example, has three significant figures but five decimal places. The guide to common IB Chemistry mistakes explains how precision errors interact with unit and data-processing mistakes.

For each calculation, write the equation, convert compatible units, substitute unrounded values, calculate using full precision, identify the limiting measurement, and round only the final result. Add the correct unit and check whether the magnitude is physically reasonable. If the question requests a stated number of significant figures, follow that instruction.

Conclusion

Significant figures prevent IB science answers from claiming unsupported precision. Count zeros carefully, use significant figures for multiplication and division, use decimal places for addition and subtraction, retain guard digits, and align measurements with their uncertainties.

RevisionDojo can help make these decisions automatic through worked questions and feedback. Use the RevisionDojo IB Questionbank to complete numerical Chemistry or Physics problems, checking the precision and unit of every final answer.

Sources and referenced URLs

• IB Chemistry specimen papers for first examinations in 2025
• IB Chemistry Questionbank
• IB Chemistry resources
• IB Question Bank for exam-style practice
• Why significant figures matter in IB Chemistry
• IB Chemistry measurement and analysis questions
• Common IB Chemistry measurement and analysis mistakes
• How to use IB Chemistry topic questions