Sig Fig Calculator with Steps

45.5147 rounded to 4 significant figures is 45.51. Keep the first four significant digits (4, 5, 5, 1), then check the next digit (4), which is less than 5, so the fourth digit stays the same.

1.50 has 3 significant figures. The digits 1 and 5 are significant, and the trailing zero after the decimal point is also significant because it indicates measured precision.

The number of significant figures depends on the digits present. All non-zero digits are significant. Zeros between non-zero digits count (e.g., 1002 has 4 sig figs). Leading zeros never count (0.0045 has 2 sig figs). Trailing zeros after a decimal point always count (2.500 has 4 sig figs). Trailing zeros in a whole number without a decimal are ambiguous (1200 could be 2, 3, or 4 sig figs). Use our calculator above to instantly count sig figs in any number.

To round to n significant figures: (1) Start from the first non-zero digit and count n digits. (2) Look at the digit immediately after. (3) If it is 5 or greater, round up; otherwise, round down. Example: 0.004736 rounded to 2 sig figs becomes 0.0047. The leading zeros are not significant. For whole numbers like 12,850 rounded to 3 sig figs, the result is 12,900. Enter any number in the calculator above and choose your desired precision to see the rounded result instantly.

For multiplication and division, the answer must have the same number of significant figures as the input with the fewest sig figs. Example: 4.56 (3 sig figs) x 1.4 (2 sig figs) = 6.384, which rounds to 6.4 (2 sig figs). This rule ensures the result is no more precise than the least precise measurement used. Our calculator applies this rule automatically and shows each step.

For addition and subtraction, the result must have the same number of decimal places as the input with the fewest decimal places. Example: 12.11 + 18.0 = 30.11, which rounds to 30.1 (1 decimal place, matching 18.0). This is different from the multiplication rule because precision in addition depends on place value, not total digit count.

Trailing zeros after a decimal point are always significant: 2.50 has 3 sig figs and 0.0300 has 3 sig figs. However, trailing zeros in a whole number without a decimal point are ambiguous: 1500 could have 2, 3, or 4 sig figs. To remove ambiguity, use scientific notation: 1.5 x 10^3 (2 sig figs), 1.50 x 10^3 (3 sig figs), or 1.500 x 10^3 (4 sig figs). Some textbooks use a trailing decimal point (e.g., 1500.) to indicate all four digits are significant.

Logarithms follow a special rule: the number of significant figures in the input determines the number of decimal places (not total sig figs) in the result. For example, log(4.00 x 10^2) = 2.602 -- the input has 3 sig figs, so the log has 3 decimal places. The integer part (the characteristic) shows order of magnitude and is not counted. For antilogarithms (10^x), the rule reverses: decimal places in the input determine sig figs in the output. This calculator handles log and ln sig fig rules automatically.

The number 100 is ambiguous -- it could have 1, 2, or 3 significant figures depending on context. If it is an exact count (e.g., 100 students), it has infinite sig figs. If it is a measurement, use scientific notation to clarify: 1 x 10^2 (1 sig fig), 1.0 x 10^2 (2 sig figs), or 1.00 x 10^2 (3 sig figs). Writing 100. with a trailing decimal point also indicates 3 sig figs in some conventions.

Significant figures prevent false precision in scientific results. Every instrument has limited accuracy, so reporting extra digits misleads readers about data quality. In chemistry, wrong sig figs in stoichiometry can cause incorrect reagent amounts. In physics, they ensure honest reporting of experimental uncertainty. Proper sig fig usage is required in lab reports, published research, and professional engineering calculations. Learning sig fig rules is essential for any science course.