Question

数 $2.5252525\ldots$ 可以写成分数。将该分数约成最简分数后，其分子与分母之和是：

The number $2.5252525\ldots$ can be written as a fraction. When reduced to lowest terms the sum of the numerator and denominator of this fraction is:

$7$

$29$

$141$

$349$

以上都不是

none of these

将循环部分 $0.525252\ldots$ 写成分母为 $99$ 的分数

Write the repeating part $0.525252\ldots$ using a denominator of $99$

加上整数部分，再约分

Add the integer part and then reduce the fraction

有 $2.525252\ldots=2+\frac{52}{99}=\frac{250}{99}\text{。}$ 这个分数已经是最简分数，并且 $250+99=349$ 。

因此，正确答案是 D。

We have $2.525252\ldots=2+\frac{52}{99}=\frac{250}{99}.$ This fraction is already in lowest terms, and $250+99=349.$

Therefore, the correct answer is D.