Sure, let's tackle each problem step-by-step and express our answers with the correct number of significant figures.
### Problem 1
Calculate the sum of [tex]\(0.091\)[/tex] and [tex]\(1.324\)[/tex].
1. Align the numbers by their decimal points:
[tex]\[
\begin{array}{r}
0.091 \\
+ 1.324 \\
\end{array}
\][/tex]
2. Perform the addition:
[tex]\[
0.091 + 1.324 = 1.415
\][/tex]
3. The number of significant figures in the sum should match the least number of decimal places in the numbers being added. Here, [tex]\(0.091\)[/tex] has three decimal places and [tex]\(1.324\)[/tex] has three decimal places. Thus, the result should have three decimal places:
[tex]\[
1.415
\][/tex]
### Problem 2
Calculate the sum of [tex]\(41.0\)[/tex] and [tex]\(78.3\)[/tex].
1. Align the numbers by their decimal points:
[tex]\[
\begin{array}{r}
41.0 \\
+ 78.3 \\
\end{array}
\][/tex]
2. Perform the addition:
[tex]\[
41.0 + 78.3 = 119.3
\][/tex]
3. The number of significant figures in the sum should match the least number of decimal places in the numbers being added. Here, [tex]\(41.0\)[/tex] has one decimal place and [tex]\(78.3\)[/tex] has one decimal place. Thus, the result should have one decimal place:
[tex]\[
119.3
\][/tex]
In summary:
[tex]\[
0.091 + 1.324 = 1.415
\][/tex]
[tex]\[
41.0 + 78.3 = 119.3
\][/tex]
