What Are Significant Figures?
Significant figures (often abbreviated sig figs) are the digits in a number that carry meaning contributing to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros when a decimal point is present. Leading zeros are never significant because they merely position the decimal point. For example, 0.004567 has four significant figures (4, 5, 6, 7), while 4500 has two unless written as 4500.0, which has five.
Scientists and engineers use significant figures to communicate the precision of measurements without implying more accuracy than the instrument provides. A ruler marked in millimeters produces measurements with a certain number of sig figs, and reporting extra digits would be misleading. For rounding to fixed decimal places instead, use our Rounding Calculator or Number Rounder.
What This Calculator Does
Enter any number and specify how many significant figures you want. The tool counts the sig figs in your input and rounds the value to the target number of significant digits. A reference table shows the number rounded to 1 through 6 sig figs for quick comparison.
- Inputs: A number and target significant figures count
- Outputs: Sig figs count in input, rounded result, and reference table
Sig Figs Rules
Non-zero digits
All non-zero digits are always significant. The number 345 has three significant figures, and 0.345 also has three.
Leading zeros
Leading zeros are never significant. They only position the decimal point. The number 0.004567 has four significant figures, not seven.
Trailing zeros
4500 has 2 sig figs (no decimal point)
4500. has 4 sig figs (decimal point present)
4500.0 has 5 sig figs (decimal point present)
Trailing zeros are significant only when a decimal point is explicitly shown. This is why scientists often write 4500. (with a trailing decimal point) to indicate four significant figures.
How to Use the Calculator
- Enter the number you want to analyze
- Set the target number of significant figures
- The sig figs count and rounded result update instantly
Example Calculation
Example: Round 0.0045678 to 3 significant figures. The leading zeros are not significant. The three significant digits are 4, 5, and 7. The fourth digit (6) is 5 or more, so the third digit rounds up: 0.0045678 rounds to 0.00457. The result preserves the same order of magnitude while expressing exactly three significant figures.
Common Mistakes to Avoid
- Counting leading zeros: The zeros in 0.0045 are not significant. Only 4 and 5 count, giving two sig figs.
- Ignoring trailing zeros with decimals: 4500.0 has five significant figures because the decimal point makes the trailing zeros significant.
- Rounding too early: Always keep full precision during intermediate calculations and round only the final result to the appropriate number of sig figs.
Related Tools
For calculating measurement error after rounding, use our Percent Error Calculator. To convert numbers to scientific notation (which naturally expresses significant figures), try our Scientific Notation Calculator.