Advanced rule
Exact Numbers and Significant Figures
Exact numbers are counted or defined values. In most chemistry and physics calculations, they do not limit the significant figures in your final reported answer.
Short answer
Exact numbers usually do not restrict significant figures. If a problem says you used 3 identical trials, the counted number 3 is exact. If you multiply by a defined conversion such as 100 cm = 1 m, that conversion is exact. The measured values determine the reported precision.
Exact vs measured values
Counted value
3 trials
Exact
The number of trials was counted, not measured, so it does not usually limit the significant figures.
Defined conversion
100 cm = 1 m
Exact
Defined metric conversions are exact, so the measured length controls the final precision.
Measured value
2.50 g
Measured
This value has 3 significant figures because the final zero after the decimal point shows measured precision.
How exact numbers affect calculations
In multiplication and division, the final answer is normally rounded to the measured value with the fewest significant figures. Exact counted numbers and defined constants are not part of that limiting count.
Example: if each measured sample has a mass of 2.50 g and you have 3 samples, the counted value 3 does not force the result to 1 significant figure. The measured mass 2.50 g controls the precision.
Lab-report-ready wording
The counted value is exact, so it does not limit the significant figures. The final answer should be rounded based on the measured values in the calculation.
Common questions
Do exact numbers have infinite significant figures?
Many textbooks describe exact numbers as having unlimited or infinite significant figures because they are not uncertain measurements.
Is a counted number exact?
Usually yes. If you count 4 samples, the 4 is exact. The measured mass, volume, time, or length values control the reported precision.
Are conversion factors exact?
Defined conversion factors are exact. Measured or experimentally determined conversion factors may not be exact, so check the context.