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Significant figures and decimal places

Edexcel IAL Physics · WPH13 Practical Skills in Physics I

Marks are regularly lost for giving too many or too few figures. The rules are simple once you know them.

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Raw data

Record every raw reading to the resolution of the instrument, and use the same number of decimal places in a column. A metre rule reading to 1 mm gives 0.450 m, not 0.45 m. A table with 1.20, 1.4 and 1.65 in one column is inconsistent and will be criticised.

Calculated values

A calculated result can only be as precise as the least precise measurement used. Give it to the same number of significant figures as the raw data with the fewest (or one more).
Processed data in tables is usually given to 3 s.f. (logarithms usually to 3 d.p., in Unit 6).
Final answers are usually 2 or 3 s.f. 'Show that' answers need at least one more s.f. than the value given.
Never round in the middle of a calculation: keep full values in your calculator.

Uncertainties

Give an uncertainty to 1 (or 2) significant figures, and give the value to the same decimal place as the uncertainty: 9.8 ± 0.2 m/s², not 9.8143 ± 0.2 m/s².

Worked example

v = 1.23 m / 0.456 s. Give v to an appropriate number of significant figures.

Calculator: 1.23 / 0.456 = 2.697368
Both data values have 3 s.f., so give 3 s.f.

Answer: v = 2.70 m/s

Key idea: Raw data to the instrument's resolution, consistent decimal places in a column. Results to the s.f. of the least precise data (usually 2 or 3). Never round mid-calculation. Uncertainty to 1 or 2 s.f.

Check yourself

Round 0.0045678 to 3 significant figures.
Show answer
0.00457. The first significant figure is the 4: 0.00457.
A length of 2.75 m is divided by a time of 1.6 s. Give the speed in m/s to an appropriate number of significant figures.
Show answer
1.7 m/s. 2.75 / 1.6 = 1.7188; the time has only 2 s.f., so 1.7 m/s.
How many significant figures are there in 0.0450?
- 3
- 2
- 4
- 5
Show answer
3. Leading zeros do not count; the trailing zero after 5 does: 4, 5, 0.
A column of lengths in a table reads 0.350, 0.40, 0.452, 0.500 (m). What is wrong?
- The values should be in cm
- There are too many readings
- The values are not in order
- The decimal places are inconsistent: 0.40 should be 0.400
Show answer
The decimal places are inconsistent: 0.40 should be 0.400. Readings to the same instrument resolution should all have the same number of decimal places.
A calculated value of g is 9.8143 m/s² with an uncertainty of 0.2 m/s². How should the result be written?
- 9.8143 ± 0.2 m/s²
- 9.8 ± 0.2 m/s²
- 10 ± 0.2 m/s²
- 9.81 ± 0.2000 m/s²
Show answer
9.8 ± 0.2 m/s². Give the uncertainty to 1 s.f. and the value to the same decimal place.
In a 'show that the density is about 2700 kg m^-3' question, a calculator gives 2736.99 kg m^-3. Which final answer is best?
- 2700 kg m^-3
- 2736.99 kg m^-3
- 3000 kg m^-3
- 2740 kg m^-3
Show answer
2740 kg m^-3. 'About 2700' is 2 s.f., so give 3 s.f.: one more than the value given, without excessive figures.
Why should you not round intermediate values in a calculation?
- Examiners only want 1 s.f. answers
- Rounding errors build up and can change the final answer
- Calculators cannot store long numbers
- It changes the units
Show answer
Rounding errors build up and can change the final answer. Examiners report lost marks where early rounding pushed the answer outside the accepted range.

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Last updated 8 November 2026. Spotted a mistake? Tell us.