Type the correct answer in each box. Solve the problems. Express your answers to the correct number of significant figures.

[tex]\[
\begin{array}{l}
\frac{2.31}{0.790} = \square \\
\left(2.08 \times 10^3\right) \times \left(3.11 \times 10^2\right) = \square \times 10^5
\end{array}
\][/tex]



Answer :

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]