Methodology

Counting significant figures

We apply the following rules in order: (1) Non-zero digits are always significant. (2) Zeros between two non-zero digits are always significant. (3) Leading zeros are never significant. (4) Trailing zeros after a decimal point are always significant. (5) Trailing zeros in whole numbers without a decimal point are flagged as ambiguous.

For ambiguous numbers like 1000, we report the minimum sig fig count (1) and display a warning that explains how to write the number unambiguously — using a trailing decimal point or scientific notation.

For scientific notation inputs, we extract the coefficient and apply the above rules to it only. The exponent is ignored for sig fig counting.

Rounding to significant figures

To round a number to n significant figures, we: (1) Find the magnitude of the number using log₁₀. (2) Compute the scaling factor to position the nth significant digit. (3) Multiply, round using JavaScript's Math.round(), and divide back. (4) Format the result to show exactly n significant digits using toFixed() where needed.

We do not apply banker's rounding (round half to even). We use standard rounding (round half up) to match the convention taught in most science courses.

Calculating expressions

For addition and subtraction: we parse the operands, count decimal places in each, identify the minimum, compute the raw result, and round to that many decimal places.

For multiplication and division: we parse the operands, count sig figs in each using our counting algorithm, identify the minimum, compute the raw result, and round to that many sig figs.

For mixed operations (containing both + and × operators), we apply the multiplication rule as a conservative approximation and note this in the output. For precise mixed-operation results, we recommend evaluating step by step.

Scientific notation conversion

To convert a number to scientific notation: (1) Find the exponent as floor(log₁₀(|n|)). (2) Compute the coefficient as n / 10^exponent. (3) Format the coefficient to show exactly k decimal places, where k = sig_figs − 1.

This ensures the coefficient has exactly the same number of significant figures as the original number.

Content accuracy

All explanatory text is reviewed by our editorial team against standard significant figure conventions from general chemistry and physics curricula (including textbooks such as Zumdahl Chemistry and Chang General Chemistry).

Last reviewed: April 2025. If you identify a discrepancy, please contact us.