Arithmetical Operations with Significant Figures

Significant figures must be tracked correctly through arithmetic, or a calculation can manufacture precision the original data never had. Two different rules apply depending on the operation:

1. Addition and subtraction -- the result keeps as many decimal places as the term with the fewest decimal places (not the fewest sig. figs. overall). Example: $3.1+1.780+2.046=6.926\to6.9$ (since $3.1$ has only one decimal place); $12.637-2.42=10.217\to10.22$ (since $2.42$ has only two decimal places).
2. Multiplication and division -- the result keeps as many significant figures as the factor with the fewest significant figures. Example: $1.21\times36.72=44.4312\to44.4$ (three sig. figs., matching $1.21$); $36.72\div1.2=30.6\to31$ (two sig. figs., matching $1.2$). …