+0

# Help with this problem, please

0
66
3

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
+6045
+1

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

.
Sep 18, 2019
#2
+1

Rom: You missed 125. So, there are 4 such integers: 5, 25, 125, 625. Or: 4 / 1005.

Sep 18, 2019
#3
+6045
+1

you're right, good catch, tired

Rom  Sep 18, 2019