What is the sum of the repeating decimals of the form 0. [img]2022m10s/ct_ve0120

游客2024-01-12 16

问题 What is the sum of the repeating decimals of the form 0.

, where c and d are digits such that c＜d and c+d = 5?

选项 A、37/99
B、21/50
C、14/33
D、123/100
E、41/33

答案 C

解析循环小数化分数：多少位循环节，分母上就有几个9。故答案为C。

由于c＜d，c+d=5，故可能的取值为{0，5}，{1，4}，{2，3}，对应分数为5/99+14/99+23/99=42/99=14/33。

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