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Physics · Chapter 2: Physical Quantities and Measurement
Significant Figures
Rules for counting significant figures, rounding off, and significant figures in calculations.
Key termRememberExampleWatch out
01Concept
No measurement is perfectly exact. The number of digits we write shows how precise the measurement is. These meaningful digits are called significant figures: all the digits that are known for certain, plus the first doubtful digit.
A metre rule (least count 0.1 cm) gives 12.6 cm: 3 significant figures. Vernier callipers (least count 0.01 cm) give 12.63 cm: 4 significant figures. The second reading is more precise.
Rules for counting significant figures
| Rule | Example | Significant figures |
|---|---|---|
| 1. All non-zero digits are significant. | 4.37 | 3 |
| 2. Zeros between non-zero digits are significant. | 2005 | 4 |
| 3. Zeros before the first non-zero digit are not significant (they only place the decimal point). | 0.0042 | 2 |
| 4. Zeros at the end after a decimal point are significant. | 3.50 | 3 |
| 5. Zeros at the end of a whole number are not clear. Use scientific notation to show them. | 1500 → 1.5 × 10³ or 1.50 × 10³ | 2 or 3 |
Rounding off
- If the next digit is less than 5, leave the last digit unchanged. 3.142 → 3.14 (3 s.f.)
- If the next digit is 5 or more, increase the last digit by 1. 2.786 → 2.79 (3 s.f.)
Significant figures in calculations
- Multiplying or dividing: the answer has as many significant figures as the least precise value. Area = 4.52 cm × 2.1 cm = 9.492 → 9.5 cm² (2 s.f.)
- Adding or subtracting: the answer has as many decimal places as the value with the fewest decimal places. 12.6 cm + 2.15 cm = 14.75 → 14.8 cm
02Virtual Lab
Try this topic for yourself in the virtual lab. It opens on its own page with steps, tasks and questions.
03Real World Examples
Cricket statistics
A batting average shown as 45.67 is calculated to 2 decimal places, but the runs and innings are exact counts, so here every digit is meaningful.
Medical reports
A blood report shows haemoglobin as 13.5 g/dL, not 13.4826: the machine is only precise to one decimal place.
Weather
The Met Office gives Karachi's temperature as 34 °C, not 34.217 °C, because the thermometers are not that precise.
04Practice Questions
Try to answer in your own words first, then open the model answer.
Short questions
Q1.What are significant figures?Show answer
Answer
Significant figures are all the accurately known digits in a measurement plus the first doubtful digit.
Q2.How many significant figures are in: (a) 0.0305 (b) 7.200 (c) 5.03 × 10⁴?Show answer
Answer
- (a) 3 (3, 0, 5)
- (b) 4 (trailing zeros after the decimal point count)
- (c) 3
Q3.Round 2.6457 to (a) 3 and (b) 2 significant figures.Show answer
Answer
- (a) 2.6457 → 2.65
- (b) 2.6457 → 2.6
Q4.A rectangle measures 6.25 cm by 3.4 cm. Find its area to the correct number of significant figures.Show answer
Answer
- Area = 6.25 × 3.4 = 21.25 cm²
- 3.4 has only 2 s.f., so the answer is 21 cm²
Q5.Why is 1.50 × 10³ m clearer than 1500 m?Show answer
Answer
Because 1500 m could have 2, 3 or 4 significant figures. 1.50 × 10³ m clearly shows 3 significant figures.
Long questions
Q6.State the rules for finding significant figures, with an example of each. Explain why a vernier calliper reading has more significant figures than a metre rule reading.Show answer
Answer
- Non-zero digits are significant: 4.37 → 3.
- Zeros between digits are significant: 2005 → 4.
- Leading zeros are not: 0.0042 → 2.
- Trailing zeros after a decimal point are: 3.50 → 3.
- Trailing zeros in a whole number are unclear; use scientific notation.
A vernier calliper has a smaller least count (0.01 cm) than a metre rule (0.1 cm), so it gives one more reliable digit: 12.63 cm (4 s.f.) instead of 12.6 cm (3 s.f.). More significant figures means a more precise measurement.