Which one of the following is the best approximation of $\frac{7.11\times 3.85}{9.09}$?

The correct option is $\frac{7\times 4}{9}$.

To find the best approximation of the given expression, we round each decimal number in the fraction to its nearest whole number (integer):

1. In the numerator, 7.11 is closest to 7 because the first decimal digit (1) is less than 5.

2. Also in the numerator, 3.85 is closest to 4 because the first decimal digit (8) is greater than or equal to 5.

3. In the denominator, 9.09 is closest to 9 because the first decimal digit (0) is less than 5.

Substituting these rounded whole numbers back into the original expression:

$\frac{7.11\times 3.85}{9.09}\approx \frac{7\times 4}{9}$

Therefore, the best approximation expression is $\frac{7\times 4}{9}$.