Answer :
To solve the problem of dividing 12.0 by 7.11 and expressing it with the correct number of significant figures, let's go through the steps:
1. Perform the Division: Start by dividing 12.0 by 7.11. The result of this division is approximately 1.6877637130801686.
2. Determine Significant Figures: In the division, the number with the fewest significant figures determines the number of significant figures in the result. Here, 12.0 has 3 significant figures (the zero counts as it's after the decimal point), and 7.11 also has 3 significant figures. Therefore, our answer should have 3 significant figures.
3. Round the Result: We need to round 1.6877637130801686 to 3 significant figures. This involves looking at the first three digits (1.68) and considering the next digit (7). Since the digit after 1.68 is 7, we round up the last considered digit:
[tex]\[
1.688 \quad \text{(rounded from 1.6877637130801686)}
\][/tex]
4. Express Correctly: After rounding, we have the answer 1.688. Looking at the options provided:
A. 1.688
B. 1.69
C. 1.7
D. 1.70
Our correctly rounded result, 1.688, exactly matches option A.
Therefore, the correct answer is A. [tex]\(1.688\)[/tex].
1. Perform the Division: Start by dividing 12.0 by 7.11. The result of this division is approximately 1.6877637130801686.
2. Determine Significant Figures: In the division, the number with the fewest significant figures determines the number of significant figures in the result. Here, 12.0 has 3 significant figures (the zero counts as it's after the decimal point), and 7.11 also has 3 significant figures. Therefore, our answer should have 3 significant figures.
3. Round the Result: We need to round 1.6877637130801686 to 3 significant figures. This involves looking at the first three digits (1.68) and considering the next digit (7). Since the digit after 1.68 is 7, we round up the last considered digit:
[tex]\[
1.688 \quad \text{(rounded from 1.6877637130801686)}
\][/tex]
4. Express Correctly: After rounding, we have the answer 1.688. Looking at the options provided:
A. 1.688
B. 1.69
C. 1.7
D. 1.70
Our correctly rounded result, 1.688, exactly matches option A.
Therefore, the correct answer is A. [tex]\(1.688\)[/tex].
