I am new here. Being a grad student, I have been brainstorming on algorithms for a while now. I appreciate any help that can be extended regarding the problem below. I have searched enough and I couldn't find any close solution to this problem. 

We have an array of sorted distinct numbers that is infinitely long. The first n numbers are fractions that are greater than 0 but less than 1. All the remaining elements are “1”s, and you are not given the value of n. You need to develop an algorithm to check if a user-given fraction F occurs in that array. Analyze the time complexity of your algorithm as a function of n. (An example for n=8 , where the 1's begin at 8th position of the array) 

My approach:
I am guessing that the best way to solve this is by employing binary search. Each time we can bring down the size of the array by half and finally, arrive at the fraction to be found. Let us assume that there are m elements in the array, including the 1's. The number of fractional elements is n. 
The time complexity of performing the binary search on the whole array is O(log(m)). Since I am asked to express the time complexity in terms of n, m = n+k (assuming that the number of 1's in the array is k) 
So the time complexity of this problem is O(log(n+k)).

Please throw in your thoughts. Thanks