Sure, let's solve these problems step-by-step and express our answers to the correct number of significant figures.
### Problem 1:
[tex]\[ 0.091 + 1.324 \][/tex]
First, we perform the addition:
[tex]\[ 0.091 + 1.324 = 1.415 \][/tex]
Now, we need to express this answer with the correct number of significant figures. The number 0.091 has 2 significant figures, and the number 1.324 has 4 significant figures. When adding or subtracting, we express the result with the number of significant places equal to the least precise number (the one with the fewest decimal places).
Here, 0.091 (2 significant figures) is the least precise, so we round 1.415 to 2 decimal places:
[tex]\[ 1.415 \approx 1.4 \][/tex]
So, the correct answer for the first problem is:
[tex]\[ \boxed{1.4} \][/tex]
### Problem 2:
[tex]\[ 41.0 + 78.3 \][/tex]
First, we perform the addition:
[tex]\[ 41.0 + 78.3 = 119.3 \][/tex]
Next, we express this answer with the correct number of significant figures. Both 41.0 and 78.3 have 3 significant figures. When adding or subtracting, just like in problem 1, we consider the number with the fewest decimal places.
Both numbers can be considered to have the same number of decimal places because they both effectively end in the tenths place. Therefore, we maintain 3 significant figures in the answer, but in this specific context of significant figures within scientific and certain mathematical operations, a slight rounding difference could occur (though the integral number would remain unchanged with presenting as 3 significant figures).
So, the final answer for the second problem is:
[tex]\[ \boxed{119.0} \][/tex]
In summary:
[tex]\[
\begin{array}{l}
0.091 + 1.324 = \boxed{1.4} \\
41.0 + 78.3 = \boxed{119.0}
\end{array}
\][/tex]
