Answer :
Sure, let's solve these problems step by step and express the answers to the correct number of significant figures.
1. Divide [tex]\( \frac{2.31}{0.790} \)[/tex]:
First, perform the division:
[tex]\[ \frac{2.31}{0.790} = 2.9240506329113924 \][/tex]
The result needs to be expressed in scientific notation with 5 significant figures. This would be:
[tex]\[ 2.92405 \times 10^0 \][/tex]
2. Multiply [tex]\( (2.08 \times 10^3) \times (3.11 \times 10^2) \)[/tex]:
First, multiply the coefficients:
[tex]\[ 2.08 \times 3.11 = 6.4648 \][/tex]
Then, add the exponents for powers of 10:
[tex]\[ 10^3 \times 10^2 = 10^{3+2} = 10^5 \][/tex]
Putting it all together:
[tex]\[ 6.4648 \times 10^5 = 646480.0 \][/tex]
Given the answer should be to the correct number of significant figures (3 significant figures from 2.08 and 3.11):
[tex]\[ 6.47 \times 10^5 = 647000 \][/tex]
### Summary:
- For [tex]\( \frac{2.31}{0.790} \)[/tex]:
[tex]\[ 2.92405 \times 10^0 \][/tex]
- For [tex]\( (2.08 \times 10^3) \times (3.11 \times 10^2) \)[/tex]:
[tex]\[ 647000 \][/tex]
So, filling in the boxes:
[tex]\[ \begin{array}{l} \frac{2.31}{0.790}=2.92405 \times 10^0 \\ \left(2.08 \times 10^3\right) \times\left(3.11 \times 10^2\right)=647000 \end{array} \][/tex]
1. Divide [tex]\( \frac{2.31}{0.790} \)[/tex]:
First, perform the division:
[tex]\[ \frac{2.31}{0.790} = 2.9240506329113924 \][/tex]
The result needs to be expressed in scientific notation with 5 significant figures. This would be:
[tex]\[ 2.92405 \times 10^0 \][/tex]
2. Multiply [tex]\( (2.08 \times 10^3) \times (3.11 \times 10^2) \)[/tex]:
First, multiply the coefficients:
[tex]\[ 2.08 \times 3.11 = 6.4648 \][/tex]
Then, add the exponents for powers of 10:
[tex]\[ 10^3 \times 10^2 = 10^{3+2} = 10^5 \][/tex]
Putting it all together:
[tex]\[ 6.4648 \times 10^5 = 646480.0 \][/tex]
Given the answer should be to the correct number of significant figures (3 significant figures from 2.08 and 3.11):
[tex]\[ 6.47 \times 10^5 = 647000 \][/tex]
### Summary:
- For [tex]\( \frac{2.31}{0.790} \)[/tex]:
[tex]\[ 2.92405 \times 10^0 \][/tex]
- For [tex]\( (2.08 \times 10^3) \times (3.11 \times 10^2) \)[/tex]:
[tex]\[ 647000 \][/tex]
So, filling in the boxes:
[tex]\[ \begin{array}{l} \frac{2.31}{0.790}=2.92405 \times 10^0 \\ \left(2.08 \times 10^3\right) \times\left(3.11 \times 10^2\right)=647000 \end{array} \][/tex]
