Counting rules
How to identify significant figures
- Every nonzero digit is significant.
- Zeros between nonzero digits are significant.
- Leading zeros before the first nonzero digit are not significant.
- Trailing zeros after a decimal point are significant.
- Whole-number trailing zeros may be ambiguous without scientific notation.
Worked example
Count significant figures in 0.00450
- Ignore the leading zeros before 4.
- Count the digits 4 and 5.
- Count the final zero because it follows a decimal and a nonzero digit.
The value 0.00450 contains 3 significant figures.
Rounding
Round to a selected number of significant figures
Start counting from the first nonzero digit. Keep the requested number of digits, then inspect the next digit to determine whether the final retained digit should increase.
Example12.345 rounded to 3 significant figures is 12.3.
Scientific notation
Clarify ambiguous trailing zeros
Scientific notation clearly communicates precision. For example, 1.20 × 10³ has three significant figures, while 1.2 × 10³ has two.
Laboratory reporting
Preserve measurement precision
Enter measured values exactly as recorded. A value such as 8.50 should not be shortened to 8.5 because the final zero communicates instrument precision.
For a complete explanation of precision rules, read the significant figures in lab reports guide.
Rounding limits
Assumptions and limitations
Significant-figure rules communicate measurement precision, but they cannot determine the true uncertainty of an instrument or experiment. The entered value must already use a meaningful decimal representation.
Exact counted quantities and defined conversion factors are not normally limited by significant figures. Intermediate calculations should retain guard digits so repeated rounding does not distort the final result.
Related tools
Related measurement calculators
Compare a measured result with an accepted reference using the Percent Error Calculator.
Express and combine measurement precision with the Measurement Uncertainty Calculator.
Questions and answers
Significant figures FAQ
What are significant figures?
Significant figures are the meaningful digits in a measured or calculated value that communicate its precision.
Are leading zeros significant?
No. Zeros before the first nonzero digit only locate the decimal point and are not significant.
Are trailing zeros significant?
Trailing zeros after a decimal point are significant. Trailing zeros in a whole number may be ambiguous unless a decimal point or scientific notation clarifies them.
When should a laboratory result be rounded?
Keep extra digits during intermediate calculations and round the final reported result according to the required precision.