Lesson 2 — Significant Figures
Significant figures (sig figs) tell us how precise a measurement is. Physics answers should not claim more precision than the data.
The rules
- Non-zero digits are significant.
- Zeros between non-zeros are significant (
2003has 4). - Leading zeros are not significant (
0.0034has 2). - Trailing zeros are significant only if there’s a decimal point (
2500.has 4;2.500has 4). - In scientific notation, the coefficient’s digits are the sig figs (
1.20 × 10^3→ 3).
Examples
| Number | Sig figs | Why |
|---|---|---|
0.02030 |
4 | Leading zeros don’t count; trailing zero after decimal does ⇒ 2-0-3-0 → 4. |
2.500 |
4 | All digits in a decimal number, including trailing zeros, are significant. |
2500. |
4 | Decimal point indicates trailing zeros are significant. |
2500 |
2 (commonly treated) | No decimal point ⇒ trailing zeros are not significant by default (unless specified by a bar/underline or scientific notation). |
2003 |
4 | Zeros between non-zeros are significant. |
0.00340 |
3 | Leading zeros don’t count; trailing zero after decimal does. |
1.20 × 10^3 |
3 | Count digits in the coefficient 1.20 only. |
9.030e-4 |
4 | Scientific notation “e” form: coefficient 9.030 has 4 sig figs. |
100. |
3 | Decimal point present ⇒ trailing zeros are significant. |
100 |
1 (or 2–3 if specified) | Without a decimal point, trailing zeros not significant by default. Use scientific notation to state precision explicitly (e.g., 1.00 × 10^2 → 3). |
12 objects (counted) |
Exact | Counting numbers and defined conversions are exact (infinite sig figs); they don’t limit precision. |
When in doubt, communicate precision with scientific notation (e.g., write 2.50 × 10^3 instead of 2500).
Try it
How many significant figures are in 0.02030?
More practice
Rounding with sig figs
Round at the end of your calculation to match the least precise measurement. Example: multiplying a 3-sf value by a 2-sf value → result should have 2 sf.