Significant Figures Calculator 2026
🔢 Interactive Sig Fig Calculator
📊 Count Significant Figures
➕ Math Operations with Sig Figs
🎯 Round to Significant Figures
1. What Are Significant Figures?
Significant figures (also called significant digits or sig figs) are the meaningful digits in a number that contribute to its precision. They include all certain digits plus one uncertain digit.
2. Rules for Counting Significant Figures
Rule 1: Non-Zero Digits
All non-zero digits are ALWAYS significant
Examples:
- 123 has 3 significant figures
- 7.89 has 3 significant figures
Rule 2: Leading Zeros
Leading zeros (zeros before non-zero digits) are NOT significant
Examples:
- 0.0025 has 2 significant figures (2 and 5)
- 0.00340 has 3 significant figures (3, 4, and trailing 0)
Rule 3: Captive Zeros
Zeros between non-zero digits ARE significant
Examples:
- 1002 has 4 significant figures
- 5.008 has 4 significant figures
Rule 4: Trailing Zeros with Decimal
Trailing zeros after decimal point ARE significant
Examples:
- 12.00 has 4 significant figures
- 0.500 has 3 significant figures
Rule 5: Trailing Zeros Without Decimal
Trailing zeros in whole numbers without decimal are ambiguous
Examples:
- 4500 has 2 significant figures (ambiguous)
- 4500. has 4 significant figures (decimal point makes them significant)
3. Mathematical Operations with Sig Figs
Addition and Subtraction Rule
Round the result to the least number of decimal places
\[\text{Result decimal places} = \min(\text{decimal places of all numbers})\]Example:
12.11 + 18.0 + 1.013 = 31.123 → 31.1 (1 decimal place)
(18.0 has only 1 decimal place, so answer rounds to 1 decimal place)
Multiplication and Division Rule
Round the result to the least number of significant figures
\[\text{Result sig figs} = \min(\text{sig figs of all numbers})\]Example:
4.56 × 1.4 = 6.384 → 6.4 (2 sig figs)
(1.4 has only 2 sig figs, so answer rounds to 2 sig figs)
4. Examples with Solutions
| Number | Sig Figs | Explanation |
|---|---|---|
| 0.00520 | 3 | Leading zeros not significant; 5, 2, 0 are significant |
| 4500.0 | 5 | Decimal point makes all digits significant |
| 1.00 × 10³ | 3 | Scientific notation clearly shows 3 sig figs |
| 25.03 | 4 | All digits including captive zero are significant |
| 0.0800 | 3 | Leading zeros not significant; 8, 0, 0 are significant |
| 602,000,000,000,000,000,000,000 | 3 | Better written as 6.02 × 10²³ (Avogadro's number) |
5. Rounding Rules
Standard Rounding Rules:
- If the digit after rounding position is less than 5: round down
- If the digit after rounding position is greater than 5: round up
- If the digit after rounding position is exactly 5: round to nearest even number (banker's rounding)
Examples:
- 2.34 rounded to 2 sig figs = 2.3
- 2.36 rounded to 2 sig figs = 2.4
- 2.35 rounded to 2 sig figs = 2.4 (round to even)
6. Scientific Notation
Scientific notation is the best way to clearly show significant figures:
\[\text{Number} = a \times 10^n\]where \(1 \leq |a| < 10\)
Examples:
- 4500 with 2 sig figs = 4.5 × 10³
- 4500 with 4 sig figs = 4.500 × 10³
- 0.00520 = 5.20 × 10⁻³ (3 sig figs)
7. Common Mistakes to Avoid
❌ Typical Errors:
- Counting leading zeros as significant (0.007 has only 1 sig fig, not 4)
- Forgetting that trailing zeros after decimal ARE significant
- Using wrong rule for addition vs multiplication
- Not rounding intermediate calculations properly
- Confusing decimal places with significant figures
- Ignoring significant figures in unit conversions
8. Real-World Applications
Where Sig Figs Matter:
- Chemistry: Measuring chemical concentrations and reactions
- Physics: Recording experimental measurements
- Engineering: Precision in manufacturing and design
- Medicine: Dosage calculations and lab results
- Research: Reporting data with appropriate precision
- Quality Control: Ensuring measurement accuracy
💡 Pro Tip for 2026
When in doubt, use scientific notation! It eliminates ambiguity about which zeros are significant. Modern scientific calculators and software default to scientific notation for precisely this reason. Always report your final answer with the correct number of significant figures to maintain measurement precision.
📚 Remember
Significant figures represent the precision of your measurement, not accuracy. A measurement can be precise (many sig figs) but not accurate (far from true value), or vice versa. Always use appropriate significant figures for your measurement tools and methods!