Knowing that $0.333 \ldots=\frac{1}{3}$, what is the irreducible fraction equivalent to $0.1333 \ldots$.
(a) $\frac{1}{13}$
(b) $\frac{1}{15}$
(c) $\frac{1}{30}$
(d) $\frac{2}{15}$
(e) $\frac{1333}{10000}$
The correct option is (d).

Solution 1: Since $1 / 3=0.333 \ldots$, it follows that

$$
0.1333 \ldots=0.333 \ldots-0.2=\frac{1}{3}-\frac{2}{10}=\frac{1}{3}-\frac{1}{5}=\frac{2}{15}
$$

Solution 2: Using simply the rule that provides the generator of a repeating decimal, we can also obtain

$$
0.1333 \ldots=\frac{13-1}{90}=\frac{12}{90}=\frac{2}{15}
$$