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 (
2003
has 4). - Leading zeros are not significant (
0.0034
has 2). - Trailing zeros are significant only if there’s a decimal point (
2500.
has 4;2.500
has 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.