AI Math Assistant
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AI provides general assistance. Always verify important calculations.
About This Calculator
Significant figures indicate the precision of a measurement, ensuring that calculated results don't imply more accuracy than the original data supports. Mishandling sig figs can lead to misleading scientific conclusions and engineering errors. This calculator identifies the number of significant figures in any value and rounds calculation results to the appropriate precision following standard scientific rules.
Quick Tips
- 1 Leading zeros are never significant; trailing zeros after a decimal point always are.
- 2 In multiplication, the result keeps the fewest sig figs of any input.
- 3 The number 1500 has 2 sig figs unless written as 1500. (with a decimal).
Example Calculation
Multiply 3.24 (3 sig figs) by 12.5 (3 sig figs).
Raw: 40.5 | Significant figures: 3 | Result: 40.5 | Rule: fewest sig figs of inputs
Rules for Counting Significant Figures
All non-zero digits are significant. Zeros between non-zero digits are significant (e.g., 105 has 3 sig figs). Leading zeros are never significant (0.0045 has 2 sig figs). Trailing zeros after a decimal point are significant (2.500 has 4 sig figs). Trailing zeros in a whole number without a decimal point are ambiguous but often considered not significant.
How to Round to Significant Figures
To round a number to N significant figures: start counting from the first non-zero digit, keep N digits, and round the last one based on the next digit. For example, rounding 0.004572 to 3 sig figs gives 0.00457. Rounding 12,345 to 3 sig figs gives 12,300.
Frequently Asked Questions
Trailing zeros after a decimal point are always significant (2.50 has 3 sig figs). Trailing zeros in a whole number without a decimal are ambiguous — 1200 might have 2, 3, or 4 sig figs depending on context. Using scientific notation removes ambiguity.
Significant figures indicate the precision of a measurement. Reporting more sig figs than your instrument can measure implies false precision. In calculations, the result should not have more sig figs than the least precise input.
Exact numbers (like counting 12 eggs or conversion factors like 1 foot = 12 inches) have infinite significant figures. They do not limit the sig figs in a calculation result.