Rules of Significant Figures

Significant figures are the digits in a measurement that carry meaningful information about precision. They include all certain digits plus one estimated digit, reflecting the accuracy of your measuring instrument. Using the correct number of significant figures ensures your reported results honestly represent measurement precision and prevents false claims of accuracy in calculations.

Count all non-zero digits as significant. Zeros between non-zero digits are significant, leading zeros are not, and trailing zeros after a decimal point are significant. For example, 0.00305 has three significant figures, while 3050 has three or four depending on whether the trailing zero is significant. Clarity improves when using scientific notation.

Accuracy describes how close a measurement is to the true value, while precision reflects how consistent repeated measurements are. A precise instrument produces repeatable results; an accurate instrument produces results near the true value. Significant figures communicate precision, not accuracy, so proper digit reporting is essential for conveying measurement quality.

When adding or subtracting, round your answer to the decimal place of the least precise measurement. For example, 12.5 plus 1.25 equals 13.75, but should be reported as 13.8 because 12.5 has only one decimal place. This rule ensures your result doesn't claim more precision than your input data supports.

When multiplying or dividing, round your answer to match the number of significant figures in the measurement with the fewest significant figures. If you multiply 4.5 by 2.1, the result 9.45 should be rounded to 9.5 because both inputs have two significant figures. This preserves the precision limit set by your least precise measurement.

Scientific notation clearly separates significant figures from place-holding zeros. Writing 3050 as 3.05 × 10³ shows three significant figures unambiguously, while 3.050 × 10³ shows four. This notation eliminates confusion about trailing zeros and makes it easy to apply significant figure rules consistently across calculations and measurements.

Avoid rounding intermediate results during multi-step calculations; keep extra digits throughout and round only the final answer. Rounding too early introduces cumulative rounding errors that reduce accuracy. Apply significant figure rules only to your final result to ensure it reflects the true precision of your original measurements and calculations.