Of course! Let's solve each problem step by step, ensuring that we express the answers to the correct number of significant figures.
1. For the first expression:
[tex]\[
\frac{2.11}{0.790}
\][/tex]
Given the numbers, [tex]\(2.11\)[/tex] has three significant figures and [tex]\(0.790\)[/tex] also has three significant figures. Therefore, the answer should be expressed to three significant figures.
The calculation result is:
[tex]\[
\frac{2.11}{0.790} = 2.671
\][/tex]
So, the correct answer, to three significant figures, is:
[tex]\[
2.671
\][/tex]
2. For the second expression:
[tex]\[
(2.08 \times 10^3) \times (3.11 \times 10^2)
\][/tex]
Let's break down the calculation in steps:
- First, multiply the coefficients (2.08 and 3.11):
[tex]\[
2.08 \times 3.11 = 6.4688
\][/tex]
- Then, multiply the powers of 10:
[tex]\[
10^3 \times 10^2 = 10^{3+2} = 10^5
\][/tex]
Therefore, the result of the multiplication is:
[tex]\[
6.4688 \times 10^5
\][/tex]
Since the original numbers have three significant figures each (2.08 and 3.11), we should express the result to three significant figures. Hence, the answer is:
[tex]\[
6.469 \times 10^5
\][/tex]
In conclusion, the correct answers are:
[tex]\[
\begin{array}{l}
\frac{2.11}{0.790} = 2.671 \\
(2.08 \times 10^3) \times (3.11 \times 10^2) = 6.469 \times 10^5
\end{array}
\][/tex]
