Every digit, justified
Significant Figures Calculator
Count, round, or evaluate — and see exactly which rule limited the answer. Handles decimals, scientific notation, and multi-step expressions with full guard digits.
0.00456
3 sig figs
0.00456
Significant figures
0.00456 has 3 significant figures.
The five counting rules
| Rule | Significant? | Example |
|---|---|---|
| Non-zero digits | Always | 123 → 3 |
| Captive zeros (between non-zeros) | Always | 4008 → 4 |
| Leading zeros | Never | 0.00456 → 3 |
| Trailing zeros with a decimal point | Yes | 1.200 → 4 |
| Trailing zeros, no decimal point | Ambiguous | 1200 → 2 (write 1.200×10³ for 4) |
Operation rules
| Operation | Rule | Example |
|---|---|---|
| Addition / subtraction | Result keeps the fewest decimal places of any term. | 41.34 + 1.561 = 42.90 |
| Multiplication / division | Result keeps the fewest significant figures of any factor. | 2.5 × 3.42 = 8.6 |
| Multi-step | Keep guard digits; round only at the final step. | (2.0 + 3.0) × 4.00 = 20 |
| Exact numbers | Counted or defined values have infinite significant figures and never limit the result. | π, 100 (defined) |