Significant Figures
Round to sig figs
About This Calculator
Significant figures (sig figs) express the precision of a measurement. Every non-zero digit is significant, and zeros may or may not be depending on their position. Sig fig rules prevent false precision from propagating through calculations — the result cannot be more precise than the least precise measurement.
Formula
Multiplication/Division: result has same sig figs as the factor with fewest sig figs
Addition/Subtraction: result has same decimal places as the least precise addend
Scientific notation always shows exact sig figs: 3.00×10² has 3 sig figs
Example Calculation
Multiply 3.45 × 12.1 (round to correct sig figs).
- 3.45 has 3 sig figs; 12.1 has 3 sig figs
- Calculator: 3.45 × 12.1 = 41.745
- Round to 3 sig figs: 41.7
Answer: 41.7 (3 significant figures)
Significant Figure Rules
| Number | Sig Figs | Reason |
|---|---|---|
| 1234 | 4 | All non-zero digits |
| 1200 | 2 or 4 | Ambiguous — use scientific notation |
| 0.0045 | 2 | Leading zeros not significant |
| 1200. | 4 | Trailing decimal point makes zeros significant |
| 1.200×10³ | 4 | Scientific notation — all digits significant |
| 100 | 1 | Only the 1 is certain |
Frequently Asked Questions
Are zeros significant?
It depends on position: leading zeros (0.0045) are not significant. Trailing zeros after a decimal point (1.200) are significant. Trailing zeros without a decimal point (1200) are ambiguous — use scientific notation to be clear.
How do sig figs apply to addition?
In addition and subtraction, align decimal points and round to the last significant decimal place of the least precise number. For example, 12.11 + 0.3 = 12.4 (not 12.41) because 0.3 has only one decimal place.
Why do sig figs matter?
They communicate measurement precision honestly. Writing 4.000 m claims precision to the nearest millimeter; writing 4 m only claims precision to the nearest meter. Mixing them in calculations introduces false precision.
What is the difference between accuracy and precision?
Accuracy is how close a measurement is to the true value; precision is how reproducible or detailed the measurement is. A measurement can be precise (consistent) but inaccurate (consistently wrong).