Core concept
What are significant figures?
Significant figures are the meaningful digits in a measured or calculated value. They communicate the precision of the measurement and prevent a result from appearing more exact than the equipment and method justify.
For example, a balance reading of 12.40 g contains four significant figures. The final zero is meaningful because it indicates the precision of the recorded measurement.
Identification rules
How to count significant figures
Nonzero digits
Every nonzero digit is significant. The value 347 contains three significant figures.
Zeros between nonzero digits
Captive zeros are significant. The value 2.07 contains three significant figures.
Leading zeros
Zeros before the first nonzero digit are not significant. The value 0.0045 contains two significant figures.
Trailing decimal zeros
Zeros at the end of a decimal value are significant. The value 6.200 contains four significant figures.
Trailing whole-number zeros
Their meaning may be ambiguous unless scientific notation or a decimal point clarifies precision.
Important distinction
Significant figures versus decimal places
Significant figures
Meaningful digits
In 0.00450, the digits 4, 5, and the final zero are significant, giving three significant figures.
Decimal places
Digits after the decimal
The value 0.00450 contains five decimal places, even though it has three significant figures.
Measurement precision
Record all justified instrument digits
A measured value should reflect the resolution of the instrument. Do not add unsupported digits, but do not remove meaningful zeros that communicate measurement precision.
ExampleA digital balance displaying 8.50 g should normally be recorded as 8.50 g, not 8.5 g.
Calculations
Multiplication and division rule
For multiplication and division, the final result should generally contain the same number of significant figures as the measured value with the fewest significant figures.
Example4.2 × 3.15 = 13.23, reported as 13 because 4.2 has two significant figures.
Calculations
Addition and subtraction rule
For addition and subtraction, round according to the least precise decimal position rather than the fewest total significant figures.
Example12.11 + 0.3 = 12.41, reported as 12.4 because 0.3 is measured to one decimal place.
Rounding
Round final results, not every intermediate step
Keep additional digits during intermediate calculations. Repeated early rounding can accumulate and produce a less accurate final result.
- Enter the original measured values.
- Complete intermediate calculations.
- Keep unrounded calculator values.
- Determine the required final precision.
- Round only the reported final result.
Scientific notation
Use scientific notation to remove ambiguity
Scientific notation makes the number of significant figures explicit, especially when a whole number ends in zeros.
Ambiguous
1500
The intended precision is unclear without additional context.
Explicit
1.50 × 10³
This notation clearly communicates three significant figures.
Exact values
Distinguish measurements from exact quantities
Counted objects and defined relationships are usually exact. For example, five test tubes is an exact count, and a defined conversion such as 1 metre equaling 100 centimetres does not normally limit the precision of a calculation.
Lab report application
Maintain precision throughout the report
- Record raw measurements at instrument precision.
- Use consistent decimal places within data columns.
- Retain extra digits during calculations.
- Round calculated results appropriately.
- Include units with every reported measurement.
- Use scientific notation for very large or small values.
- Avoid mixing differently rounded versions of the same result.
Common mistakes
Significant-figure problems to avoid
- Adding digits that the instrument did not measure.
- Removing meaningful trailing zeros.
- Confusing significant figures with decimal places.
- Rounding every intermediate calculation.
- Using inconsistent precision in a table column.
- Reporting calculator output without evaluation.
- Leaving units out of calculated results.
Related guides
Apply precision to experimental results
Review how measurements and calculations should be presented in the Lab Report Results guide, or review the full structure in the Lab Report Format guide.
Questions and answers
Significant figures FAQ
Why are significant figures used in lab reports?
Significant figures communicate measurement precision and prevent calculated results from appearing more exact than the experimental data support.
Are significant figures and decimal places the same?
No. Significant figures count meaningful digits from the first nonzero digit, while decimal places count digits appearing after the decimal point.
When should a calculated result be rounded?
Keep extra digits during intermediate calculations and round the final reported result according to the least precise relevant measurement.
Are exact counted values limited by significant figures?
Exact counts and defined conversion factors generally do not limit significant figures because they are not measured values with experimental uncertainty.