To solve the given problems and express the answers to the correct number of significant figures, follow these steps:
### Problem 1:
[tex]\[
\frac{2.31}{0.790} = \square
\][/tex]
1. Identify the number of significant figures in each number:
- 2.31 has 3 significant figures.
- 0.790 also has 3 significant figures.
2. Perform the division:
[tex]\[
\frac{2.31}{0.790} \approx 2.924
\][/tex]
3. Round the result to the correct number of significant figures:
Since both numbers have 3 significant figures, the result should also have 3 significant figures.
[tex]\[
2.924 \text{ rounded to 3 significant figures } = 2.92
\][/tex]
Thus, the answer to the first problem is:
[tex]\[
\frac{2.31}{0.790} = 2.92
\][/tex]
### Problem 2:
[tex]\[
(2.08 \times 10^3) \times (3.11 \times 10^2) = \square \times 10^5
\][/tex]
1. Identify the number of significant figures in each number:
- 2.08 has 3 significant figures.
- 3.11 also has 3 significant figures.
2. Perform the multiplication:
[tex]\[
(2.08 \times 10^3) \times (3.11 \times 10^2) = 2.08 \times 3.11 \times 10^{3+2} = 6.4688 \times 10^5
\][/tex]
3. Round the result to the correct number of significant figures:
Since both numbers have 3 significant figures, the result should also have 3 significant figures.
[tex]\[
6.4688 \text{ rounded to 3 significant figures } = 6.47
\][/tex]
Thus, the answer to the second problem is:
[tex]\[
(2.08 \times 10^3) \times (3.11 \times 10^2) = 6.47 \times 10^5
\][/tex]
In summary, the solutions to the problems are:
[tex]\[
\frac{2.31}{0.790} = 2.92
\][/tex]
[tex]\[
(2.08 \times 10^3) \times (3.11 \times 10^2) = 6.47 \times 10^5
\][/tex]
