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If $\frac{a}{b}$ is the probability that the reciprocal of a randomly selected positive odd integer less than 2010 gives a terminating decimal, with $a$ and $b$ being relatively prime positive integers, what is $a+b$?

 Sep 18, 2019
 #1
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\(\text{The set of odd integer reciprocals with a terminating decimal representation}\\ \text{is just the set of odd integers that are powers of 5.}\\ \text{ Between 1 and 2010 This is 5,25,625}\\ \text{There are a total of 1005 odd integers less than 2010 so }\\ p = \dfrac{3}{1005}\\ 3+1005=1008\)

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 Sep 18, 2019
 #2
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Rom: You missed 125. So, there are 4 such integers: 5, 25, 125, 625. Or: 4 / 1005.

 Sep 18, 2019
 #3
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+1

you're right, good catch, tired

Rom  Sep 18, 2019

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