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Overview
Significant figures, often called significant digits, are the meaningful digits in a measured or calculated value. They communicate the precision of a measurement and help prevent false exactness in scientific reporting.
In physics, a calculated answer should not claim more precision than the measurements used to produce it. Significant figures are one way to preserve honesty in numerical work.
Why Significant Figures Matter
Measurements come from instruments, and instruments have limits. If a ruler measures to the nearest millimeter, it does not justify an answer reported to twelve decimal places. Excess digits can make a result look more reliable than it is.
Significant figures help align the answer with the quality of the evidence. They are not decorative formatting. They are part of scientific communication.
Counting Significant Figures
Nonzero digits are significant. Zeros between nonzero digits are significant. Leading zeros before the first nonzero digit are not significant because they only locate the decimal point.
Trailing zeros may or may not be significant depending on notation. A decimal point or scientific notation can clarify whether a zero is intended as measured precision.
Multiplication and Division Rule
For multiplication and division, the final answer is usually reported with the same number of significant figures as the measured value with the fewest significant figures.
This rule reflects the idea that the least precise measurement limits the precision of the result.
Addition and Subtraction Rule
For addition and subtraction, the final answer is usually reported to the same decimal place as the least precise measurement.
This is different from the multiplication and division rule because addition and subtraction are limited by place value rather than total digit count.
Common Mistakes
A common mistake is to round too early. Intermediate calculations should usually keep extra digits, while the final answer is rounded at the end.
Another mistake is confusing significant figures with decimal places. They are related, but they are not the same. Significant figures count meaningful digits, while decimal places count positions after the decimal point.