How can I turn a floating point number into the closest fraction represented by a byte numerator and denominator?

Question

How can I write an algorithm that given a floating point number, and attempts to represent is as accurately as possible using a numerator and a denominator, both restricted

Answer 1

How worried are you about efficiency? If you're not calling this conversion function 100s of times per second or more, then it probably wouldn't be all that hard to brute-force through every possible denominator (most likely only 255 of them) and find which one gives the closest approximation (computing the numerator to go with the denominator is constant time).