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Round any number to a chosen count of significant figures.
Round any number to a chosen count of significant figures.
Enter values above and click Calculate — results will appear here with the formula explained.
Significant figures communicate measurement confidence: reporting 12.34 cm implies precision to hundredths that a ruler reading of 12 cm doesn't possess. Rounding to sig figs trims digits that measurements never actually delivered.
Counting rules trip everyone initially: leading zeros never count (0.00456 has three), captive zeros always do (405 has three), trailing zeros count only after a decimal point (120 has two; 120. has three). Scientific notation sidesteps ambiguity — 1.20 × 10² unambiguously carries three.
Multiplication and division versus addition and subtraction follow different propagation rules: for ×/÷, the result carries the fewest sig figs of any input (12.34 × 0.56 = 6.9 with 2 sig figs), while for +/− the result carries the fewest decimal places (12.34 + 0.56 = 12.90). Mixing the rules is where grade points vanish.
Exactly how trailing zeros are handled separates careful reporting from sloppy: 2,500 without a decimal is ambiguous (2 sig figs), 2,500. with a decimal is 3, 2.50 × 10³ is 3, and 2.500 × 10³ is 4. Labs use scientific notation to make the count explicit rather than hoping readers guess.
When to round matters as much as how: rounding intermediate steps compounds error. Carry one extra guard digit through calculations, then round the final answer to the appropriate sig figs. Early rounding on a 5-step chain can shift the last digit by several units.
Sig figs are not just pedagogy — they govern real decisions: reporting a pollutant at 0.00457 ppm (3 sig figs) versus 0.0046 (2) changes whether a threshold is crossed, and engineering tolerances live or die on the same distinction.
In practice, report results with the same precision as the limiting measurement: a 12.3 cm length (3 sig figs) times 4.56 cm (3) yields 56.1 cm², not 56.088 — the extra digits imply false certainty.
Lab reports and engineering drawings enforce sig figs contractually: a dimension written as 12.30 cm (4 sig figs) carries a tighter tolerance than 12.3 cm (3), even though the numbers look similar. Writing an extra zero is a claim about measurement capability, not a stylistic choice.
Round any number to a chosen count of significant figures. Formula: round to n sig figs: identify leading-digit position, keep n digits, round remainder. Example: 0.004567 to three sig figs: leading zeros don't count, so keep 4, 5, 6 and round → 0.00457.
Significant figures communicate measurement confidence: reporting 12.34 cm implies precision to hundredths that a ruler reading of 12 cm doesn't possess. Rounding to sig figs trims digits that measurements never actually delivered.
Counting rules trip everyone initially: leading zeros never count (0.00456 has three), captive zeros always do (405 has three), trailing zeros count only after a decimal point (120 has two; 120. has three). Scientific notation sidesteps ambiguity — 1.20 × 10² unambiguously carries three.
Multiplication and division versus addition and subtraction follow different propagation rules: for ×/÷, the result carries the fewest sig figs of any input (12.34 × 0.56 = 6.9 with 2 sig figs), while for +/− the result carries the fewest decimal places (12.34 + 0.56 = 12.90). Mixing the rules is where grade points vanish.
Exactly how trailing zeros are handled separates careful reporting from sloppy: 2,500 without a decimal is ambiguous (2 sig figs), 2,500. with a decimal is 3, 2.50 × 10³ is 3, and 2.500 × 10³ is 4. Labs use scientific notation to make the count explicit rather than hoping readers guess.
When to round matters as much as how: rounding intermediate steps compounds error. Carry one extra guard digit through calculations, then round the final answer to the appropriate sig figs. Early rounding on a 5-step chain can shift the last digit by several units.
Sig figs are not just pedagogy — they govern real decisions: reporting a pollutant at 0.00457 ppm (3 sig figs) versus 0.0046 (2) changes whether a threshold is crossed, and engineering tolerances live or die on the same distinction.
In practice, report results with the same precision as the limiting measurement: a 12.3 cm length (3 sig figs) times 4.56 cm (3) yields 56.1 cm², not 56.088 — the extra digits imply false certainty.
Lab reports and engineering drawings enforce sig figs contractually: a dimension written as 12.30 cm (4 sig figs) carries a tighter tolerance than 12.3 cm (3), even though the numbers look similar. Writing an extra zero is a claim about measurement capability, not a stylistic choice.
0.004567 to three sig figs: leading zeros don't count, so keep 4, 5, 6 and round → 0.00457. Then 12.34 × 0.56 = 6.9 (2 sig figs, limited by 0.56).
Formulas are standard public references (see our methodology). External standards are cited in the text where they apply.
Last reviewed: September 2026 · Report an error