33.53 The number $2.5252525 \cdots \cdots$ can be written as a fraction. When simplified, the sum of the numerator and denominator of this fraction is
(A) 7 .
(B) 29 .
(C) 141 .
(D) 349 .
(E) None of the above.
(11th American High School Mathematics Examination, 1960)
[Solution 1] Let $x=2.525252 \cdots \cdots$, then $100 x=252.5252 \cdots \cdots$ so $100 x-x=250$, we get $x=\frac{250}{99}$, and $250+99=349$. Therefore, the answer is $(D)$.
[Solution 2] From $2.525252 \cdots \cdots=2 . \dot{5} \dot{2}=2 \frac{52}{99}=\frac{250}{99}$, hence the answer is $(D)$.