Let's simplify the expression step by step:

$\frac{9 \times 9}{99} \div 11$

1. First, calculate $9 \times 9 = 81$.
2. Then divide $81$ by $99$:

$\frac{81}{99} = \frac{9}{11} \quad \text{(simplified by dividing both the numerator and denominator by 9)}$

3. Now, divide $\frac{9}{11}$ by 11:

$\frac{9}{11} \div 11 = \frac{9}{11 \times 11} = \frac{9}{121}$

So the result is:

$\frac{9}{121} \quad \text{or} \quad 0.0743801653$

Would you like a more detailed explanation or help with a related topic? Here are some follow-up questions:

1. How do you simplify fractions in general?
2. Can you convert a fraction to a decimal and vice versa?
3. What is the rule for dividing fractions?
4. How can you handle large numbers in calculations?
5. Can you use this approach to solve more complex problems?

Tip: Always check if you can simplify fractions early in a problem—it often makes the math easier to manage!