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What is the sum of the repeating decimals of the form 0. [img]2022m10s/ct_ve0120
What is the sum of the repeating decimals of the form 0. [img]2022m10s/ct_ve0120
游客
2024-01-12
4
管理
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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