Question E.4: Significant Figures in Calculations Perform each calculation...
Significant Figures in Calculations
Perform each calculation to the correct number of significant figures.
(a) 1.10 × 0.5120 × 4.0015 ÷ 3.4555
(b) 0.355
+ 105.1
\underline{- 100.5820}
(c) 4.562 × 3.99870÷ (452.6755 – 452.33)
(d) (14.84 × 0.55) – 8.02
(a) Round the intermediate result (in blue) to three significant figures to ref lect the three significant figures in the least precisely known quantity (1.10).
1.10 × 0.5120 × 4.0015 ÷ 3.4555
= 0.65219
= 0.652
(b) Round the intermediate answer (in blue) to one decimal place to reflect the quantity with the fewest decimal places (105.1). Notice that 105.1 is not the quantity with the fewest significant figures, but it has the fewest decimal places and therefore determines the number of decimal places in the answer.
\begin{array}{r |c}\begin{matrix}0.3 \\+105.1\\-100.5 \end{matrix}&\begin{matrix} 55\\\\820 \end{matrix} \\ \hline \begin{matrix} 4.8 \end{matrix}&\begin{matrix} 730 \end{matrix} \end{array} \begin{matrix} \\\\\\=4.9 \end{matrix}(c) Mark the intermediate result to two decimal places to ref lect the number of decimal places in the quantity within the parentheses having the smallest number of decimal places (452.33). Round the final answer to two significant figures to reflect the two significant figures in the least precisely known quantity (0.3\underline{4}55 ).
(d) Mark the intermediate result to two significant figures to reflect the number of significant figures in the quantity within the parentheses having the smallest number of significant figures (0.55). Round the final answer to one decimal place to reflect the one decimal place in the least precisely known quantity (8.\underline{1}62 ).
(14.84 × 0.55) – 8.02 = 8.\underline{1}62 – 8.02
= 0.142
= 0.1