To solve the problem of dividing 12.0 by 7.11 and expressing the result to the correct number of significant figures, let's follow these steps:
1. Perform the division:
[tex]\[
\frac{12.0}{7.11} \approx 1.6877637130801686
\][/tex]
2. Determine the significant figures:
- The number 12.0 has three significant figures.
- The number 7.11 also has three significant figures.
3. Express the result to the appropriate number of significant figures:
- The result of the division, 1.6877637130801686, needs to be rounded to three significant figures because both the dividend and the divisor have three significant figures.
4. Round the result for three significant figures:
- Rounding 1.6877637130801686 to three significant figures, we get 1.69. The crucial fourth digit, which is 7, rounds the number up.
Therefore, the correct choice for the problem [tex]\(\frac{12.0}{7.11}\)[/tex] expressed to the correct number of significant figures is:
[tex]\[
\boxed{1.69}
\][/tex]
Hence, the correct answer is B.
