I once encountered a situation where I had a floating-point number, probably 10 or 12 decimal places long, but I suspected that it was actually a rounded-off version of some rational number with not-too-big denominator (less than 1000). How can I find (or at least guess) the rational number? What I did was to start computing (in Excel, which tells you something about my programming skills) the continued fraction of my floating-point number. For a while, the integers I got were reasonably small ones, but then I got one that was way bigger than the previous ones. So I said: That must be the rounded-off version of $\infty$. In other words, I replaced that big integer with $\infty$, which amounts to cutting off the continued fraction at that step. The resulting finitely long continued fraction is, of course, rational, and it gave the answer I wanted. (Later, I checked with a number theorist, and he confirmed that this is how one should attack such questions.)