What is Significant figures?

The significant figures of a measured number are the digits actually vouched for by the measurement: all written digits except the leading zeros. Trailing zeros count — $5.20 \times 10^{-3}\,\mathrm{s}$ (three significant figures) promises more than $5.2 \times 10^{-3}\,\mathrm{s}$ (two). Scientific notation shows the count at a glance: the mantissa carries exactly the significant figures.

The significant figures of a written number are its digits from the first non-zero one: $0.0820$ has three, $8.20 \times 10^{-2}$ the same three, $820$ is ambiguous (two or three) unless written $8.2 \times 10^{2}$ or $8.20 \times 10^{2}$. A result is written with the significant figures its uncertainty allows (Method 1.20 below): not “$g = 9.7723\,\mathrm{m}/\mathrm{s}^{2}$” when the fourth digit is unknown.