Which of the fractions below is closest to 1?

Step 1 (Define Closeness to 1): The closeness of a fraction $x$ to 1 is determined by the absolute difference $|x-1|$. The smaller the absolute difference, the closer the fraction is to 1.

Step 2 (Calculate the Distances): We evaluate the absolute difference for each option in ['8/7', '9/10', '10/11', '11/10']:

1. $\left|\frac{8}{7}-1\right|=\frac{1}{7}\approx 0.1428$

2. $\left|\frac{9}{10}-1\right|=\frac{1}{10}=0.1000$

3. $\left|\frac{10}{11}-1\right|=\frac{1}{11}\approx 0.0909$

4. $\left|\frac{11}{10}-1\right|=\frac{1}{10}=0.1000$

Step 3 (Compare the Distances): Comparing the absolute differences:

Thus, $\frac{10}{11}$ has the smallest distance to 1, and is the closest fraction.

Step 4 (Conclusion): This corresponds to option index 2. The correct answer is 2.