Definition and Rules of Significant Figures

The significant figures (or significant digits) of a measured value are the digits known reliably, plus exactly one more digit that is uncertain. For instance, the gravitational constant is quoted as $G=6.67\times10^{-11}$ N m$^2$ kg$^{-2}$: the digits $6$ and $6$ are reliable, while the final $7$ is the one uncertain digit -- so the value has three significant figures.

Table 1.9 sets out the counting rules: every non-zero digit counts; a zero between two non-zero digits counts; a trailing zero to the left of a decimal point counts; a trailing zero with no decimal point does not count unless it is known to come from an actual measurement; a leading zero (before the first non-zero digit, in a number less than 1) never counts; a trailing zero after a decimal point (and after a non-zero digit) always counts; and -- crucially -- the count is completely independent of which unit or which power-of-ten prefix is used to express the number (e.g. $1.53$ cm, $0.0153$ m, and $0.0000153$ km are the same physical length, all with three significant figures). An exact counting number (like the '2' in $S=2\pi r$) is not a measured quantity at all, so it is treated as having infinitely many significant …