Solve the problems. Express your answers to the correct number of significant figures.

[tex]\[
\begin{array}{l}
\frac{2.11}{0.790}=\square \\
\left(2.08 \times 10^3\right) \times\left(3.11 \times 10^2\right)=\square \times 10^5
\end{array}
\][/tex]



Answer :

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]