Subsection1.1.2Mathematical Operations with Significant Figures
Addition or subtraction: The final result should retain as many decimal places as there are in the number with the least decimal places. For example, the sum of the numbers 436.32 g, 227.2 g and 0.301 g is 663.821 g by mere arithmetic addition but the least precise measurement (227.2 g) is correct to only one decimal place. Therefore, the final result should be rounded off to 663.8 g. Similarly, the difference in length can be expressed as:
\begin{equation*}
0.307\, m - 0.304\,y m = 0.0025=0.003 \,m.
\end{equation*}
Multiplication or division: The final result should retain as many significant figures as are there in the original number with the least significant figures. For example, if mass of an object is measured to be, say, 4.237 g (four significant figures) and its volume is measured to be \(2.51 \,cm^3\) , then its density, by mere arithmetic division, is \(1.68804780876 \,g/cm^3 \) upto 11 decimal places. But density should be reported to three significant figures as
\begin{equation*}
density = \frac{4.237g}{2.51 \,cm^3} = 1.69\,cm^3.
\end{equation*}
