A probability problem by Cosmic Curiosity
Probability
Level
3
The reciprocals of how many numbers from 1 to 100 have terminating decimals?
The answer is 15.
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1 solution
The logic is simple. A reciprocal will have terminating decimals if the denominator can be made 10 to the power n (where n can be any natural number). This will be true when the number can be written as 5 to the power n or 2 to the power n (as 100= 2 to the power 2 multiplied by 5 to the power 2). Hence the set of numbers whose reciprocal have terminating decimals are- {1,2,4,5,8,10,16,20,25,32,40,50,64,80,100} which are 15. Thus the answer is 15.