Let's solve the quotient $\frac{1}{0.3}$.

First, convert the decimal $0.3$ to a fraction. We know that $0.3$ is equivalent to $\frac{3}{10}$.

Now, dividing 1 by $0.3$ is the same as multiplying 1 by the reciprocal of $\frac{3}{10}$:

$\frac{1}{0.3} = 1 \times \frac{10}{3} = \frac{10}{3}.$

Now, perform the division $10 \div 3$. This results in:

$\frac{10}{3} = 3.3333\ldots$

This is a repeating decimal, where the digit "3" repeats.

Therefore, the correct answer is: $1 \div 0.3 = 3.\overline{3}.$

So, the correct choice is:

B. The answer is a repeating decimal. $1 \div 0.3 = 3.\overline{3}$

Would you like more details on how I approached this problem?

Here are some related questions:

1. How do you convert a decimal to a fraction?
2. What is the meaning of a repeating decimal?
3. How do you find the reciprocal of a fraction?
4. What is a terminating decimal, and how is it different from a repeating decimal?
5. How do you multiply fractions?

Tip: When dividing by a decimal, converting it to a fraction can simplify the calculation.