Sure, let's solve each problem step-by-step.
1. For the division problem:
[tex]\[ \frac{2.31}{0.790} = \square \][/tex]
We need to divide 2.31 by 0.790.
The result of this division, expressed to the correct number of significant figures, is:
[tex]\[ \frac{2.31}{0.790} = 2.924 \][/tex]
2. For the multiplication problem:
[tex]\[ (2.08 \times 10^3) \times (3.11 \times 10^2) = \square \times 10^5 \][/tex]
First, multiply the coefficients:
[tex]\[ 2.08 \times 3.11 = 6.4688 \][/tex]
Next, multiply the powers of 10:
[tex]\[ 10^3 \times 10^2 = 10^5 \][/tex]
So the multiplication result in scientific notation, expressed to the correct number of significant figures, is:
[tex]\[ (2.08 \times 10^3) \times (3.11 \times 10^2) = 6.469 \times 10^5 \][/tex]
To summarize, the solutions are:
[tex]\[ \frac{2.31}{0.790} = 2.924 \][/tex]
[tex]\[ (2.08 \times 10^3) \times (3.11 \times 10^2) = 6.469 \times 10^5 \][/tex]
