Sure, let's solve the problems step by step.
1. First Calculation:
[tex]\[
\frac{2.31}{0.30}
\][/tex]
To perform the division:
[tex]\[
\frac{2.31}{0.30} = 7.7
\][/tex]
The result is [tex]\( 7.7 \)[/tex] to the correct number of significant figures (two significant figures as in the divisor).
2. Second Calculation:
[tex]\[
\left(2.08 \times 10^3\right) \times \left(3.11 \times 10^2\right)
\][/tex]
To perform the multiplication of numbers in scientific notation:
1. Multiply the coefficients (the base numbers):
[tex]\[
2.08 \times 3.11 = 6.4488 \approx 6.45
\][/tex]
We round the result to three significant figures, because [tex]\(2.08\)[/tex] and [tex]\(3.11\)[/tex] both have three significant figures.
2. Add the exponents:
[tex]\[
3 + 2 = 5
\][/tex]
Putting it all together:
[tex]\[
(2.08 \times 10^3) \times (3.11 \times 10^2) = 6.45 \times 10^5
\][/tex]
To summarize the solutions:
[tex]\[
\frac{2.31}{0.30} = 7.7
\][/tex]
[tex]\[
\left(2.08 \times 10^3\right) \times \left(3.11 \times 10^2\right) = 6.47 \times 10^5
\][/tex]
So the correct answers to fill in the boxes are:
[tex]\[
\boxed{7.7}
\][/tex]
[tex]\[
\boxed{6.47} \times 10^5
\][/tex]
