Significant figures
01 // Why they matter
Significant figures are the digits in a measurement that carry real meaning about its precision, including all certain digits plus one estimated digit. If a graduated cylinder is marked every 1 mL, reporting a reading as 24.638 mL claims a precision the tool cannot actually provide — the reading should stop at 24.6 mL.
When you calculate with measured numbers (adding, multiplying), the answer can only be as precise as your least precise measurement. Rounding a calculated result to the right number of significant figures keeps a lab report honest about how precise the data really was.
02 // Counting rules
| Rule | Example | Sig figs |
|---|---|---|
| All non-zero digits count | 247 | 3 |
| Zeros between non-zero digits count | 1005 | 4 |
| Leading zeros never count | 0.0034 | 2 |
| Trailing zeros count only with a decimal point | 1500 | 2 (unless written 1500.) |
| Trailing zeros after a decimal point count | 2.50 | 3 |
03 // Worked example
Multiply a length by a width measured with different precision, then round the result correctly.
| Length | 12.5 cm (3 sig figs) |
| Width | 4.2 cm (2 sig figs) |
Formula For multiplication/division, round the answer to match the fewest significant figures of any measurement used.
04 // Questions people ask
Do zeros always count as significant figures?
Not always. Leading zeros (like the zeros in 0.0034) never count. Zeros between other digits always count. Trailing zeros only count when there is a decimal point present, like the zero in 2.50.
How many significant figures should a final lab answer have?
For multiplication or division, match the number of significant figures in the least precise measurement used in the calculation. For addition or subtraction, match the fewest decimal places instead.
Why not just report every digit a calculator shows?
Because a calculator does not know how precise your original measurements were — it will happily give you ten digits from a measurement that was only accurate to two. Reporting more digits than your tools can support overstates your precision.