Sure, let's solve these problems step by step and express the answers to the correct number of significant figures.
1. Divide [tex]\( \frac{2.31}{0.790} \)[/tex]:
First, perform the division:
[tex]\[
\frac{2.31}{0.790} = 2.9240506329113924
\][/tex]
The result needs to be expressed in scientific notation with 5 significant figures. This would be:
[tex]\[
2.92405 \times 10^0
\][/tex]
2. Multiply [tex]\( (2.08 \times 10^3) \times (3.11 \times 10^2) \)[/tex]:
First, multiply the coefficients:
[tex]\[
2.08 \times 3.11 = 6.4648
\][/tex]
Then, add the exponents for powers of 10:
[tex]\[
10^3 \times 10^2 = 10^{3+2} = 10^5
\][/tex]
Putting it all together:
[tex]\[
6.4648 \times 10^5 = 646480.0
\][/tex]
Given the answer should be to the correct number of significant figures (3 significant figures from 2.08 and 3.11):
[tex]\[
6.47 \times 10^5 = 647000
\][/tex]
### Summary:
- For [tex]\( \frac{2.31}{0.790} \)[/tex]:
[tex]\[
2.92405 \times 10^0
\][/tex]
- For [tex]\( (2.08 \times 10^3) \times (3.11 \times 10^2) \)[/tex]:
[tex]\[
647000
\][/tex]
So, filling in the boxes:
[tex]\[
\begin{array}{l}
\frac{2.31}{0.790}=2.92405 \times 10^0 \\
\left(2.08 \times 10^3\right) \times\left(3.11 \times 10^2\right)=647000
\end{array}
\][/tex]
