Significant figures are the digits in a measurement result that carry reliable information, reflecting the actual precision of the instrument or method used.
Discover FizziQ
How to measure it in class
Steps:
- Open FizziQ and note the number of decimals displayed by the pressure sensor (e.g., 1013.25 hPa: 6 digits). Then observe the light sensor (e.g., 342 lux: 3 digits).
- Record 20 consecutive pressure measurements and observe which digits remain stable and which fluctuate. Stable digits are significant; fluctuating digits are uncertain.
- Calculate the mean and standard deviation of the measurements. Compare the number of significant figures justified by the standard deviation with the number displayed by the sensor.
- Write the result correctly: value ± uncertainty, with the proper number of significant figures.
Scientific activities on this topic
Several experiments easily performed with a smartphone, tablet, or computer allow you to understand significant figures in real measurement situations.
- 1: Uncertainty - Analyzing measurement uncertainties: https://www.fizziq.org/en/activities/uncertainty/
- 2: Evaluating Sensor Quality - Analyzing sensor precision: https://www.fizziq.org/en/activities/evaluate-the-quality-of-a-sensor/
- 3: Period of a Pendulum - Building a device to precisely determine the period of a pendulum: https://www.fizziq.org/en/activities/period-of-a-pendulum/
Learn more
Historical origin of conventions
Significant figure rules were formalized in the 19th century with the development of metrology. Before that, scientists often wrote all digits their instruments displayed without considering reliability. With Gauss and Laplace’s error theory, the scientific community understood the importance of keeping only digits carrying real information.
Scientific notation and significant figures
Scientific notation is the clearest way to indicate significant figures. Writing 2.0 × 10³ clearly indicates two significant figures, where “2000” is ambiguous. In science, scientific notation removes this ambiguity.
Significant figures and digital tools
Calculators and spreadsheets often display 10-15 digits for any result, creating a dangerous illusion of precision. Teaching students to round correctly is as important as the calculation itself.
International rules
The Guide to the Expression of Uncertainty in Measurement (GUM), published by BIPM, recommends expressing results as value ± uncertainty, with uncertainty to one or two significant figures.
Formula
For multiplication or division: the result has as many significant figures as the data with the fewest.
For addition or subtraction: the result has as many decimal places as the data with the fewest.
Example: 3.24 × 2.1 = 6.804 → rounded to 6.8 (two significant figures, like 2.1).
Application examples
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A GPS indicating a distance of 1.234 km when its precision is ±10 m displays too many significant figures
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A doctor who reports a weight of 72 kg rather than 72.384 kg correctly uses significant figures
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A cook measuring 250 ml of water with a measuring cup graduated every 50 ml has only one useful significant figure
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An analog speedometer indicating approximately 90 km/h has two significant figures
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A smartphone stopwatch displaying 12.347 s does not guarantee this precision if the trigger is manual
FAQ
Q: How do you count the significant figures of a number? A: All digits are significant except leading zeros. Examples: 0.0045 has 2 significant figures, 3.20 has 3, and 1,000 has between 1 and 4 depending on context.
Q: Why don’t leading zeros count? A: Leading zeros are merely decimal position indicators. Writing 0.003 or 3 × 10⁻³ expresses the same value with the same number of significant figures (just one).
Q: Should intermediate results be rounded? A: No. Keep all digits during calculations and only round the final result. Rounding at each step accumulates rounding errors.
Q: How many significant figures for an uncertainty? A: Uncertainty is expressed with one or two significant figures. By convention, use one digit, unless it starts with 1 or 2, in which case keep two.
Q: What is the link between significant figures and uncertainty? A: The number of significant figures in a result should reflect its uncertainty. If the uncertainty is ±0.5, writing a result with three decimal places makes no sense.
Related concepts
Uncertainty - Precision - Resolution - Scientific notation - Rounding - Measurement error - Standard deviation