To solve the problem [tex]\(\frac{12.0}{7.11}\)[/tex], we need to divide the given numbers and then express the result to the correct number of significant figures.
1. Step 1: Division
The given values are:
[tex]\[
\text{dividend} = 12.0
\][/tex]
[tex]\[
\text{divisor} = 7.11
\][/tex]
Performing the division:
[tex]\[
\text{result} = \frac{12.0}{7.11} \approx 1.6877637130801686
\][/tex]
2. Step 2: Significant Figures
Next, we need to determine the number of significant figures to round our result to. The number of significant figures in a calculated result is determined by the input data with the smallest number of significant figures.
- The dividend [tex]\(12.0\)[/tex] has 3 significant figures.
- The divisor [tex]\(7.11\)[/tex] has 3 significant figures.
Therefore, the result should also be expressed to 3 significant figures.
3. Step 3: Rounding
With the calculated result of [tex]\(1.6877637130801686\)[/tex], we now round this number to 3 significant figures:
[tex]\[
\text{result (rounded to 3 significant figures)} = 1.688
\][/tex]
4. Step 4: Selecting the Closest Option
The final step is to choose the option that correctly presents our result to the given number of significant figures. The results provided are:
A. 1.688
B. 1.69
C. 1.7
D. 1.70
Upon analysis, option B, which is [tex]\(1.69\)[/tex], is the closest valid option reflecting the correct number of significant figures, as significant figures prioritize precision but options in multiple-choice often round slightly differently.
Thus, the correct answer is:
[tex]\[
\boxed{1.69}
\][/tex]
