Sure! Let's solve these problems step by step, making sure to express the answers to the correct number of significant figures.
### Problem 1: Division
[tex]\[
\frac{2.31}{0.790} = \square
\][/tex]
To divide these numbers:
- We have two values: 2.31 (3 significant figures) and 0.790 (3 significant figures).
- When performing division, the result should have the same number of significant figures as the number with the fewest significant figures.
The division of 2.31 by 0.790 gives:
[tex]\[
\frac{2.31}{0.790} = 2.9240506329113924
\][/tex]
Since both 2.31 and 0.790 have three significant figures, we round the result to three significant figures:
[tex]\[
\frac{2.31}{0.790} = 2.92
\][/tex]
### Problem 2: Multiplication and Scientific Notation
[tex]\[
(2.08 \times 10^3) \times (3.11 \times 10^2) = \square \times 10^5
\][/tex]
To solve this:
- We multiply the coefficients together:
[tex]\[
2.08 \times 3.11 = 6.4688
\][/tex]
2.08 has three significant figures, and 3.11 has three significant figures; therefore, our product should be rounded to three significant figures.
- Multiplying the powers of 10 together:
[tex]\[
10^3 \times 10^2 = 10^{3+2} = 10^5
\][/tex]
So, the complete multiplication gives us:
[tex]\[
(2.08 \times 10^3) \times (3.11 \times 10^2) = 6.4688 \times 10^5
\][/tex]
Rounding 6.4688 to three significant figures:
[tex]\[
6.4688 \approx 6.47
\][/tex]
Therefore:
[tex]\[
(2.08 \times 10^3) \times (3.11 \times 10^2) = 6.47 \times 10^5
\][/tex]
Hence, the final answers are:
[tex]\[
\begin{array}{l}
\frac{2.31}{0.790} = 2.92 \\
(2.08 \times 10^3) \times (3.11 \times 10^2) = 6.47 \times 10^5
\end{array}
\][/tex]
