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 $a+b$?

Guest Sep 18, 2019

#1**+1 **

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

.Rom Sep 18, 2019