## Multiplication and division of measured numbers

When multiplying several quantities, the number of significant figures in the final answer is the same as the number of significant figures in the quantity having the smallest number of significant figures. The same rule applies to division. Example 1 The length of a rectangular is 4.12\ m and the width is 5.0\ m, find the area. A = L times W =4.12\ m times 5.0\ m =21\ m^2 Example 2 The radius of the circle is 6.00 times 10^(-2)\ m, find the area. A = πr^2 = π(6.00 times 10^(-2))^2 = 113 times 10^(-4) = 1.13 times 10^(-2)\ m^2 Example 3 A rectangular playground has a length of (25 ± 0.2) m and a width of (10 ± 0.1) m. Calculate the area of the playground, including its uncertainty. Area: A = WL = 25\ m times 10\ m = 250 m^2 Uncertainty: (∆A)/A =(∆L)/L + (∆W)/W (∆A) =((∆L)/L + (∆W)/W)A ∆A = (0.2 / 25 + 0.1/10) times 250 m^2 = 4.5\ m^2≈ 5\ m^2 Answer (250 ± 5) m^2