To solve $\frac{1}{0.9}$, we can convert it to a fraction:

$\frac{1}{0.9} = \frac{1}{\frac{9}{10}} = \frac{1 \times 10}{9} = \frac{10}{9}$

Now, we can convert $\frac{10}{9}$ to a decimal:

$\frac{10}{9} = 1.1111\ldots$

This is a repeating decimal with the digit 1 repeating. So, the answer is:

$1.\overline{1}$

The correct choice is: C. The answer is a repeating decimal, $1.\overline{1}$.

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Do you want more details, or do you have any questions?
Here are some related questions you can explore:

1. What is the result of $\frac{1}{0.8}$?
2. How can you convert $\frac{5}{6}$ to a decimal?
3. What is $\frac{1}{0.7}$ as a repeating decimal?
4. How do you convert a repeating decimal to a fraction?
5. What is $\frac{1}{0.6}$ in decimal form?

Tip: When dividing by a decimal, you can multiply both the numerator and the denominator by 10 to eliminate the decimal before performing division.