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

You should look at the Farey Sequence.
Given a limit on the denominator d, the Farey Sequence is every fraction having denominator <= d.

Then, you would simply take your float and compare it to the resolved value of the Farey fraction. This will allow you to represent your float in terms of repeating-decimal reals.

Here is a page on its implementation in java:
http://www.merriampark.com/fractions.htm

Here is a good demonstration of their use:
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fractions/fareySB.html