Answer :

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]