Count sig figs, round to any precision, and see which digits are significant.
Significant figures (sig figs) are the digits in a number that carry meaningful information about its precision. In science, engineering, and statistics, the number of significant figures indicates how precisely a measurement was made. A laboratory balance reading 12.34 grams (4 sig figs) is more precise than one reading 12 grams (2 sig figs). Reporting more digits than your measurement supports implies false precision, while reporting fewer discards real information.
Rule 1: All nonzero digits are significant. 1234 has 4 sig figs. 56.78 has 4 sig figs.
Rule 2: Zeros between nonzero digits ("captive zeros") are significant. 1002 has 4 sig figs. 3.07 has 3 sig figs.
Rule 3: Leading zeros are never significant. They are placeholders only. 0.0034 has 2 sig figs. 0.00001 has 1 sig fig.
Rule 4: Trailing zeros after a decimal point are significant. 2.50 has 3 sig figs. 100.0 has 4 sig figs. 0.00340 has 3 sig figs.
Rule 5: Trailing zeros in a whole number without a decimal point are ambiguous. 1500 could be 2, 3, or 4 sig figs depending on context. To make the precision explicit, use scientific notation: 1.5 x 10³ (2 sig figs), 1.50 x 10³ (3 sig figs), or 1.500 x 10³ (4 sig figs).
Multiplication and division: The result should 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, rounded to 6.4 (2 sig figs).
Addition and subtraction: The result should have the same number of decimal places as the input with the fewest decimal places. Example: 12.11 (2 decimal places) + 18.0 (1 decimal place) = 30.11, rounded to 30.1 (1 decimal place).
These rules ensure that calculation results never claim more precision than the least precise measurement used. The Scientific Notation Converter helps express numbers with unambiguous sig fig counts.
In chemistry, using incorrect sig figs can lead to miscalculated reagent quantities. In engineering, false precision in measurements can create a misleading sense of accuracy that masks real uncertainty. In physics labs, students are routinely graded on correct sig fig usage in their calculations and lab reports. The concept is simple but the application requires care, especially in multi-step calculations where intermediate rounding can compound errors. Best practice is to carry one or two extra sig figs through intermediate steps and round only the final answer.
Exact numbers have infinite significant figures and never limit the precision of a calculation. Exact numbers include counted quantities (12 eggs, 3 trials), defined conversions (1 meter = 100 centimeters, 1 inch = 2.54 centimeters exactly), and mathematical constants used in their exact form. Only measured quantities have limited sig figs. In the calculation "3 samples x 4.56 grams each," the 3 is exact and the result should have 3 sig figs (from 4.56), giving 13.7 grams.