If 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?
Do you understand your question and what is being asked of you to find out? I'm not quite certain but here is my attempt. Let me know your thinking.
1 - How many "positive odd integers" are there between 1 and 2010? There are: 2010 / 2 =1005. right?
2 -Of those 1005 "positive odd integers", how many do you think have their reciprocals end in a terminating decimal?
3 - My understanding, correct me if I'm wrong, is that only: 5^1 =5, 5^2 =25, 5^3 =125, and 5^4 =625, or a total of 4 integers have that property.
4 - What is the probability of randomly picking one of these 4 integers out of a total of 1005 "positive odd integers"?
5 - Well, It is: 4 / 1005, which are "relatively prime", that is, their GCD = 1
6 - Therefore, a =4 and b=1005 and a + b =4 + 1005 =1009 .
7 - Did you understand all of the above and what do you think? Let me know if I went astray somewhere !.
