To solve these problems, we'll perform the arithmetic operations and then adjust the results to the correct number of significant figures.
1. For [tex]\(410 - 52\)[/tex]:
- Perform the subtraction: [tex]\(410 - 52 = 358\)[/tex].
- Adjust to the correct number of significant figures:
- 410 has 3 significant figures.
- 52 has 2 significant figures.
- The result should be limited to 2 significant figures because the least precise number (52) has 2 significant figures.
- Therefore, [tex]\(358\)[/tex] should be rounded to [tex]\(360\)[/tex].
2. For [tex]\(3.054 + 1.16\)[/tex]:
- Perform the addition: [tex]\(3.054 + 1.16 = 4.2139999999999995\)[/tex].
- Adjust to the correct number of significant figures:
- 3.054 has 3 decimal places.
- 1.16 has 2 decimal places.
- The result should be limited to 2 decimal places because the least precise number (1.16) has 2 decimal places.
- Therefore, [tex]\(4.2139999999999995\)[/tex] should be rounded to [tex]\(4.21\)[/tex].
So, the final answers with the correct number of significant figures are:
[tex]\[
\begin{array}{l}
410 - 52 = 360 \\
3.054 + 1.16 = 4.21
\end{array}
\][/tex]
