Let's solve the given problems, making sure to express the answers to the correct number of significant figures:
1. Division Problem:
[tex]\[
\frac{2.31}{0.79} = ?
\][/tex]
To solve this, we perform the division:
[tex]\[
\frac{2.31}{0.79} = 2.924
\][/tex]
The answer should be rounded to three significant figures:
[tex]\[
\frac{2.31}{0.79} = 2.92 \, (\text{rounded to three significant figures})
\][/tex]
2. Multiplication Problem:
[tex]\[
\left(2.08 \times 10^3\right) \times \left(3.11 \times 10^2\right) = ?
\][/tex]
First, perform the multiplication of the two numbers directly:
[tex]\[
(2.08 \times 10^3) \times (3.11 \times 10^2) = 6.4688 \times 10^5
\][/tex]
Here, ensure that the answer is expressed in scientific notation to the correct number of significant figures. Since [tex]\(2.08\)[/tex] has three significant figures and [tex]\(3.11\)[/tex] has three significant figures, the result should be expressed with three significant figures too:
[tex]\[
6.4688 \times 10^5 \text{ rounded to three significant figures is } 6.47 \times 10^5
\][/tex]
So, the answers to the problems are:
[tex]\[
\begin{array}{l}
\frac{2.31}{0.790} = 2.92 \\
\left(2.08 \times 10^3\right) \times \left(3.11 \times 10^2\right) = 6.47 \times 10^5
\end{array}
\][/tex]
