How this calculator works
- Step 1Find the firstfirst non-zero digitLeading zeros only place the point.
- Step 2Countevery digit after itTrailing zeros count after a point.
- Step 3Roundlook at the next digitA lone 5 rounds to even.
Significant figures show how precisely a number was measured. They start at the first non-zero digit. Zeros between digits always count; zeros at the end count only when a decimal point shows they were measured.
The calculator works on your digits exactly as typed, so trailing zeros are never lost to floating-point arithmetic.
Worked example: OpenStax’s rounding rules
- Rule
look at the first dropped digit
- 18.3384dropped 3 < 5: round down18.3
- 0.028675dropped 7 > 5: round up0.0287
- 92.85exactly 5: round to even92.8
- 6.87525 then 2: round up6.88
Read the result
- 0.008324076 figuresLeading zeros never count.
- 1300 vs 1.30e32 vs 3Scientific notation removes the doubt.
Rounding a lone 5 to the even digit avoids always pushing results upward when many values are rounded.
Assumptions and limits
- OpenStax rulesCounting and rounding as in Chemistry 2e, 1.5.
- Trailing point100. is read as three figures.
- Exact numbersCounted items have unlimited figures.
- Exact digitsNo floating-point rounding.
Related precision tools
Significant figures show how precise a measurement is. Rounding rules and notation follow from it.
To round by decimal places or a chosen rule, use the rounding calculator. The scientific notation calculator writes values compactly, and the percent error calculator compares a measurement with its expected value.
Common mistakes
Mistake: Counting leading zeros.
Instead: Start at the first non-zero digit.
Mistake: Dropping trailing zeros after a point.
Instead: 55.0 has three figures, not two.
Checking the method
A separate script counts and rounds every golden value with Python’s Decimal and round-half-even, reproducing OpenStax’s examples.
Read how we test our calculators, or browse more maths calculators.