Significant Figures Calculator
Three tools in one. Count the sig figs in any number with a digit-by-digit breakdown, round a value to exactly N significant figures, or apply the correct sig-fig rules to arithmetic operations. Every step is explained.
Calculator Mode
Presets
Supports decimals, leading/trailing zeros, and scientific notation (e.g. 1.20e-3).
Results
Significant Figures
Digit-by-Digit Breakdown
Rules Applied
- Leading zeros before the first non-zero digit are never significant.
- All non-zero digits (2) are significant.
- Trailing zero after the last non-zero digit are significant because a decimal point is present.
Reference Guide
Non-Zero Digits and Captive Zeros
Every non-zero digit in a number is always significant. The digits 1 through 9 always count toward the total.
A zero that sits between two non-zero digits is called a captive zero and is always significant. In 1207, the zero between 2 and 7 is significant, giving 4 significant figures.
- 47 has 2 sig figs (both non-zero)
- 1207 has 4 sig figs (captive zero counts)
- 3.0042 has 5 sig figs (two captive zeros)
Leading Zeros, Trailing Zeros, and the Decimal Point
Leading zeros (zeros before the first non-zero digit) are never significant. They are only placeholders. In 0.0045, the three leading zeros are not significant.
Trailing zeros are significant only when there is an explicit decimal point in the number.
- 0.0045 has 2 sig figs (leading zeros not significant)
- 100.0 has 4 sig figs (trailing zeros after decimal count)
- 100. has 3 sig figs (trailing decimal makes all digits significant)
- 0.00120 has 3 sig figs (leading zeros excluded, trailing zero counts)
Ambiguous Integers and Scientific Notation
An integer like 1200 is ambiguous. The trailing zeros might be significant (if the measurement was precise to the ones place) or might just be placeholders. By convention, they are treated as not significant, but the number is flagged as ambiguous.
Scientific notation removes all ambiguity. Write 1.2 x 10^3 for 2 sig figs, 1.20 x 10^3 for 3, or 1.200 x 10^3 for 4.
- 1200 is ambiguous, treated as 2 sig figs
- 1200. has exactly 4 sig figs
- 1.20e3 has exactly 3 sig figs
Rounding to Significant Figures
To round to N significant figures, keep the first N significant digits and drop the rest. The digit immediately after the last kept digit determines whether to round up or keep the value.
If that next digit is 5 or greater, round up. If it is 4 or less, round down (keep the last kept digit unchanged).
- 4567 rounded to 2 sig figs is 4600 (or 4.6 x 10^3)
- 0.004567 rounded to 2 sig figs is 0.0046
- 9.99 rounded to 2 sig figs is 10.
- 2.345 rounded to 3 sig figs is 2.35 (round-half-up)
Multiplication and Division Rule
When multiplying or dividing measured quantities, the result should have the same number of significant figures as the measurement with the fewest significant figures.
The least precise measurement sets the limit on precision for the final answer.
- 4.56 x 1.4 = 6.384 rounded to 2 sig figs = 6.4 (limited by 1.4)
- 10.0 / 3.0 = 3.333... rounded to 2 sig figs = 3.3
- 2.50 x 3.000 = 7.50 (limited by 2.50, which has 3 sig figs)
Addition and Subtraction Rule
When adding or subtracting measured quantities, the result should have the same number of decimal places as the measurement with the fewest decimal places.
Precision here is determined by the position of the last significant digit, not by the count of sig figs.
- 12.11 + 0.3 = 12.41 rounded to 1 decimal place = 12.4
- 100 + 0.1 = 100.1 rounded to 0 decimal places = 100
- 5.25 - 1.2 = 4.05 rounded to 1 decimal place = 4.1
