Round to N Significant Figures

How to round to significant figures

Significant figures measure precision from the first nonzero digit, not from the decimal point. Leading zeros only locate the decimal and do not count. Zeros between significant digits count, and zeros written after a decimal can state measured precision. This is why rounding 0.004567 to three significant figures gives 0.00457: the first significant digit is 4, even though it appears several places after the decimal point.

For a nonzero value x and a target of N significant figures, first find m = floor(log10(|x|)), the power of ten occupied by the first significant digit. The final retained place is p = m - (N - 1). Round x to the nearest multiple of 10^p using the selected method. The calculator applies that rule with decimal strings and integer operations, so it does not inherit binary floating-point surprises such as 1.005 appearing slightly below its exact decimal value.

1. Ignore the sign temporarily and locate the first nonzero digit.
2. Count N digits from that point. The Nth digit is the last retained digit.
3. Inspect the complete discarded part, not only a rounded intermediate value.
4. Apply the chosen tie or directed-rounding rule, then restore the sign.
5. Write enough digits, preferably in scientific notation, to make the precision visible.

Worked examples

Rounding method comparison

Most inputs give the same answer under the three nearest-value methods. They differ only on an exact tie: a discarded 5 followed entirely by zeros. Ceiling, floor, and truncation are directed methods; any nonzero discarded part can matter.

Half-even is useful across large datasets because repeated exact ties do not always move in one direction. Half-up remains the common classroom default. ASTM conformance work can impose a specified practice, so use the method named by the governing standard instead of assuming a universal default.

Trailing zeros and scientific notation

An integer such as 1200 is visually ambiguous in ordinary notation: it may communicate two, three, or four significant figures depending on context. After rounding to three significant figures, write 1.20e3 or 1.20 x 10^3 when the precision matters. The zero after the 2 is then visibly part of the coefficient. The calculator shows decimal notation for familiarity and scientific and E notation for an unambiguous record.

Do not confuse significant figures with decimal places. Rounding 0.00456 to two significant figures produces 0.0046, which has four decimal places. Rounding the same value to two decimal places would produce 0.00. The target here always starts at the first significant digit.

Calculation method and limits

The server renderer parses the mantissa and exponent as strings, locates the retained and discarded digits, and performs carry propagation one decimal character at a time. The browser uses an exact BigInt rational implementation. Neither path sends the number through a binary JavaScript or PHP float. Inputs are limited to one numeric literal, 1,000 mantissa digits, an exponent from -1,000 to 1,000, and a target from 1 to 100 significant figures so a pasted value cannot request unbounded work.

This tool rounds a stated value; it does not decide how many figures an experiment justifies. Measurement uncertainty, instrument resolution, exact conversion factors, and course or laboratory rules determine the appropriate target. Carry guard digits through a calculation and round once at the end unless a governing method explicitly says otherwise.

Related tools

Use the Significant Figures Calculator for arithmetic expressions and rule attribution, open the Sig Fig Counter to see which digits count, or compare this answer with the Round to N Decimal Places tool.