Significant Figures Calculator
Round to significant figures and identify which digits count as significant.
Results
What Are Significant Figures?
Significant figures (also called significant digits or sig figs) are the meaningful digits in a number that carry precision. They indicate how accurately a number is known. In scientific and engineering work, the number of sig figs in a result should match the precision of the least precise measurement used in the calculation.
Rules for Counting Significant Figures
1. All non-zero digits are significant (1–9). 2. Zeros between non-zero digits are significant (e.g., 1002 has 4 sig figs). 3. Leading zeros (before the first non-zero digit) are NOT significant (0.0045 has 2 sig figs). 4. Trailing zeros after a decimal point ARE significant (2.50 has 3 sig figs). 5. Trailing zeros in a whole number without a decimal are ambiguous (200 could have 1, 2, or 3 sig figs — scientific notation clarifies).
Rounding to Significant Figures
To round to N sig figs: find the Nth significant digit, look at the next digit, and round up if it's 5 or more. Example: 0.004567 to 3 sig figs — the three sig figs are 4, 5, 6 — next digit is 7 ≥ 5 — round up to 0.00457.
Sig Figs in Calculations
Multiplication/division: the result should have the same number of sig figs as the input with the fewest sig figs. Addition/subtraction: the result should have the same number of decimal places as the input with the fewest decimal places.
Worked Example: Chemistry Calculation
A student measures a sample mass as 12.3 g (3 sig figs) and a volume as 4.52 mL (3 sig figs). Density = 12.3 / 4.52 = 2.7212... g/mL. Since both inputs have 3 sig figs, the answer rounds to 3 sig figs: 2.72 g/mL. Reporting 2.7212 g/mL would imply more precision than the measurements support.
| Number | Sig Figs | Reason |
|---|---|---|
| 0.00450 | 3 | Leading zeros not significant; trailing zero after decimal is |
| 1002 | 4 | Zero between non-zero digits is significant |
| 200 | 1 (ambiguous) | Trailing zeros without decimal are ambiguous |
| 2.00 × 10² | 3 | Scientific notation removes ambiguity |
| 7,500. | 4 | Decimal point present makes trailing zeros significant |
Frequently Asked Questions
3 significant figures: 4, 5, and the trailing 0 after the decimal. Leading zeros are never significant.
Trailing zeros after a decimal point are significant (2.50 has 3 sig figs). Trailing zeros in a whole number without a decimal are ambiguous — use scientific notation to clarify (2.0 × 10² = exactly 200 with 2 sig figs).
Decimal places count digits after the decimal point. Significant figures count meaningful digits regardless of position. 0.0045 has 2 sig figs but 4 decimal places.
They communicate the precision of measurements. Reporting 3.140 suggests precision to the thousandths place; reporting 3.1 suggests precision only to the tenths. Using more sig figs than your measurement supports implies false precision.
The first 3 sig figs are 1, 2, 3. The next digit is 4 (less than 5), so round down: 12300. In scientific notation: 1.23 × 10⁴.
For addition/subtraction, match the fewest decimal places, not sig figs. Example: 12.11 + 0.3 = 12.41 → round to 1 decimal place (from 0.3) → 12.4. This is different from the rule for multiplication where you match the fewest sig figs.
1000 without a decimal could mean 1, 2, 3, or 4 sig figs. To specify exactly 2 sig figs, write 1.0 × 10³. To specify 4 sig figs, write 1000. (with a decimal point) or 1.000 × 10³. Scientific notation is the standard solution for removing this ambiguity.