Answer :
Sure, let's solve each of these problems step-by-step.
### Problem 1: Division
We need to compute \(\frac{2.31}{0.790}\).
1. Take the numerator, 2.31.
2. Take the denominator, 0.790.
3. Divide the numerator by the denominator to get the result.
So, \(\frac{2.31}{0.790} = 2.9240506329113924\).
The answer to the first problem is approximately \(2.92\) when rounded to the correct number of significant figures.
### Problem 2: Multiplication
We need to compute \((2.08 \times 10^3) \times (3.11 \times 10^2)\).
1. Multiply the significant figures: \(2.08 \times 3.11\).
2. Multiply the powers of 10: \(10^3 \times 10^2 = 10^{3+2} = 10^5\).
3. Combine these results.
So, \(2.08 \times 3.11 = 6.4688\).
The combined result is \(6.4688 \times 10^5\).
So the answer to the second problem is \(\boxed{6.47} \times 10^5\) when rounded to the correct number of significant figures.
Combining these together:
[tex]\[ \begin{array}{l} \frac{2.31}{0.790} = \boxed{2.92} \\ \left(2.08 \times 10^3\right) \times \left(3.11 \times 10^2\right) = \boxed{6.47} \times 10^5 \end{array} \][/tex]
These are the detailed solutions for the given problems.
### Problem 1: Division
We need to compute \(\frac{2.31}{0.790}\).
1. Take the numerator, 2.31.
2. Take the denominator, 0.790.
3. Divide the numerator by the denominator to get the result.
So, \(\frac{2.31}{0.790} = 2.9240506329113924\).
The answer to the first problem is approximately \(2.92\) when rounded to the correct number of significant figures.
### Problem 2: Multiplication
We need to compute \((2.08 \times 10^3) \times (3.11 \times 10^2)\).
1. Multiply the significant figures: \(2.08 \times 3.11\).
2. Multiply the powers of 10: \(10^3 \times 10^2 = 10^{3+2} = 10^5\).
3. Combine these results.
So, \(2.08 \times 3.11 = 6.4688\).
The combined result is \(6.4688 \times 10^5\).
So the answer to the second problem is \(\boxed{6.47} \times 10^5\) when rounded to the correct number of significant figures.
Combining these together:
[tex]\[ \begin{array}{l} \frac{2.31}{0.790} = \boxed{2.92} \\ \left(2.08 \times 10^3\right) \times \left(3.11 \times 10^2\right) = \boxed{6.47} \times 10^5 \end{array} \][/tex]
These are the detailed solutions for the given problems.
