Significant Figures

What "Significant Figures" Actually Record

Every measured value carries some uncertainty (Section 1.8), and the way that uncertainty is

honestly communicated in writing is through significant figures: all the digits that are

reliably known, plus exactly one further digit that is the first uncertain (estimated) digit.

For example, if a pendulum's period is reported as $1.62$ s, the digits $1$ and $6$ are

certain, and the digit $2$ is the first uncertain digit — so the measurement has three

significant figures. Reporting an extra digit beyond this, e.g. "$1.620$ s" from an instrument

that genuinely could not resolve the third decimal place, would be misleading — it

falsely implies a level of precision the instrument never achieved.

Rules for Counting Significant Figures

A key consequence of Rule 3 combined with Rule 4: changing the unit a measurement is expressed in never changes its number of significant figures. A length of $2.50$ cm (3

significant figures) remains 3 significant figures whether written as $0.0250$ m or

$25.0$ mm — only the position of the decimal point (and the count of non-significant leading

zeros) changes, never the count of meaningful digits.

Significant Figures in Calculations

• Multiplication / division: the result is rounded to the same number of significant figures as the input with the fewest significant figures. …