Quote:

Well, I'd first check to see if the divisor * 100000 is less than the number being divided. If it is, then I'd multiply what I'm dividing by by 100000 and when I increment the current number of runs where the subtraction is greater than 0, increment it by 100000.

It's not that I think the idea is terrible. It's just that it is too unreliable and slow. I am hoping to come up with some solution that has a big-O of n or n*m instead of infinity. Looping possibly endlessly (absolute worst case) to keep multiplying (another big-O of n*m not to mention the resources it consumes) simply to compare is just feels too brute-force.
Quote:

Then, once it's below 0, divide by 10, increment by 10000, etc.

You do see that this would cause my division to be recursive right? If I have a 20 digit denominator and I keep multiplying to get up to the numerator then divide my 20+ digits by 10, the 10 will be multiplied continuously until it reaches that 20+ digits at which point it will be divided by 10.