The only reasonable way to compare rationals is the decimal expansion of the string.
Why decimal? I don’t see why any other integer base wouldn’t work, and, on about any system, doing 2^n for any n > 0* will be both easier to implement and faster to run.
And that, more or less, is what the suggested solution does. It first compares the first 53 bits and, if that’s not conclusive, it compares 64 bits.
Also, of course, if your number has more than n bits, you’d only generate digits until you know the answer.
https://en.wikipedia.org/wiki/Floating-point_arithmetic#Accu...
Careful, someone is liable to throw this in an LLM prompt and get back code expanding the ASCII characters for string values like "1/346".