🎯Significant Figures Calculator
Count significant figures in a number, round to any number of sig figs, and evaluate arithmetic expressions (e.g. 5.13×3.78) while automatically applying significant figures rules. Shows step-by-step sig fig rules for multiplication, division, addition, and subtraction.
Prefer to skip the form? Scroll down and Ask AI Instead. Just describe your situation and let AI handle the math for you in seconds.
Result (Sig Figs Applied)
19.4
✦ Ask AI Instead
Significant Figures Calculator: Count, Round, and Apply Sig Fig Rules
Significant figures (sig figs) indicate the precision of a measurement. The number 0.00450 has 3 significant figures (4, 5, and the trailing 0 after the decimal — the leading zeros are not significant). In calculations, the result can only be as precise as the least precise measurement: 5.13 × 3.78 = 19.3914 → 19.4 (3 sig figs, matching the inputs).
Rules: ×÷ → min sig figs of factors | +− → min decimal places of addends
| Number | Sig Figs | Reason |
|---|---|---|
| 0.00450 | 3 | Leading zeros not sig; trailing zero after decimal IS sig |
| 1.020 | 4 | Zero between digits sig; trailing zero after decimal sig |
| 1300 | 2* | *Ambiguous: trailing zeros in integers — use 1.3×10³ for clarity |
Significant figures communicate measurement precision in science and engineering. This calculator counts sig figs in any number, rounds to any number of significant figures, and evaluates expressions (like 5.13×3.78) while automatically applying sig fig rules for multiplication/division and addition/subtraction.
Rules for Counting Significant Figures
1. All non-zero digits are significant. 1,234 → 4 sig figs. 5.67 → 3 sig figs.
2. Zeros between non-zero digits are significant. 1.002 → 4 sig figs. 30,004 → 5 sig figs.
3. Leading zeros are NOT significant. They only indicate the decimal position: 0.0042 → 2 sig figs (same as 4.2 × 10⁻³).
4. Trailing zeros after the decimal point ARE significant. They indicate measured precision: 1.50 → 3 sig figs (we measured to the hundredths). 0.00400 → 3 sig figs.
5. Trailing zeros in whole numbers are ambiguous. 1300 could be 2, 3, or 4 sig figs. Use scientific notation to be explicit: 1.3×10³ (2 sig figs), 1.30×10³ (3 sig figs), 1.300×10³ (4 sig figs).
Sig Fig Rules for Calculations
For multiplication and division: the result has the same number of sig figs as the factor with the fewest sig figs. Example: 5.13 × 3.7 = 18.981 → 18.981 has 5 digits, but 3.7 has only 2 sig figs → round to 19 (2 sig figs). If both have 3 sig figs (like 5.13 × 3.78 = 19.3914): round to 3 sig figs → 19.4.
For addition and subtraction: the result has the same number of decimal places as the addend with the fewest decimal places. Example: 12.4 + 1.056 = 13.456 → 12.4 has 1 decimal place, 1.056 has 3 → round to 1 decimal place → 13.5.
Frequently Asked Questions
How many significant figures does 0.00450 have?
0.00450 has 3 significant figures: 4, 5, and the trailing 0. The three leading zeros (0.00) are not significant — they only show the decimal position and would disappear in scientific notation (4.50 × 10⁻³, clearly 3 sig figs). The trailing zero after the decimal IS significant because it was deliberately written, indicating the measurement was made to the hundred-thousandths place. If it were written as 0.0045, it would have only 2 sig figs.
What are the rules for significant figures in multiplication and division?
The result of multiplication or division should have the same number of significant figures as the factor with the fewest significant figures. Examples: 4.56 × 1.4 = 6.384 → round to 2 sig figs (limited by 1.4) → 6.4. 100.0 / 3.7 = 27.027... → round to 2 sig figs (limited by 3.7) → 27. 2.341 × 5.2 × 1.3 = 15.77156 → limited by 5.2 and 1.3 (each 2 sig figs) → round to 2 sig figs → 16. The key: multiplication and division rules use sig fig count, not decimal places.
What are the rules for significant figures in addition and subtraction?
The result of addition or subtraction should have the same number of decimal places as the addend with the fewest decimal places. Examples: 12.4 + 1.056 = 13.456 → 12.4 has 1 decimal place → round to 1 → 13.5. 12.56 − 0.4 = 12.16 → 0.4 has 1 decimal place → round to 1 → 12.2. 450 + 23.6 = 473.6 → 450 has no decimal places → round to ones place → 474. The key: addition and subtraction rules use decimal places, not sig fig count.
How do I round a number to 3 significant figures?
Find the first 3 significant digits. The 4th digit determines rounding: if ≥5, round up the 3rd digit; if <5, leave it. Examples: 12,345 → first 3 sig figs are 1, 2, 3; 4th digit is 4 (< 5) → 12,300. 0.006789 → first 3 sig figs are 6, 7, 8; 4th is 9 (≥5) → round up → 0.00679. 1.0049 → first 3 sig figs: 1, 0, 0; 4th is 4 (<5) → 1.00. Notice that zeros can be sig figs when they're between non-zero digits or after the decimal point.
Why do significant figures matter in science?
Significant figures prevent false precision — reporting more digits than your measurement actually supports. If you measure a mass as 2.5 g (2 sig figs, implying ±0.05 g) and a length as 10.23 cm (4 sig figs), the density calculation 2.5/10.23 = 0.24437... should be reported as 0.24 g/cm³ (2 sig figs). Writing 0.2444 g/cm³ implies a precision you don't have. The rule: measurements can only be as reliable as the least precise instrument used. In labs, sig figs are used to honestly communicate instrument precision and avoid misleading calculations.