$33 \cdot 52$ Write the repeating decimal $0.363636 \cdots \cdots$ as a fraction in lowest terms, the sum of its numerator and denominator is
(A) 15 .
(B) 45 .
(C) 114 .
(D) 135 .
(E) 150 .
(16th American High School Mathematics Examination, 1965)
[Solution] $0.363636 \cdots \cdots=0.36=\frac{36}{99}=\frac{4}{11}$. Therefore, the answer is $(A)$.
Note: Generally, a repeating decimal with an $n$-digit repeating cycle can be converted to $0 . \dot{a}_{1} a_{2} \cdots \dot{a}_{n}=\frac{a_{1} a_{2} \cdots a_{n}}{99 \cdots 9}$ (the denominator consists of $n$ nines).