Orders of Magnitude, Estimation, and Significant Figures

Physicists frequently need to reason quickly about the size of a quantity without performing an exact calculation. Two related skills make this possible: working with orders of magnitude and making sensible estimations. Alongside these, the correct use of significant figures ensures that the precision we claim in a result honestly reflects the precision of our data.

Orders of magnitude

The order of magnitude of a number is the power of ten closest to it. To find it, write the number in scientific notation $a \times 10^{n}$ and round: if the coefficient $a$ is less than about $5$ (more precisely, less than $\sqrt{10} \approx 3.16$), the order of magnitude is $10^{n}$; otherwise it rounds up to $10^{n+1}$. For example, the mass of a human, roughly $70\ \text{kg} = 7 \times 10^{1}\ \text{kg}$