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This is in both common lisp (clisp and sbcl) and scheme (guile). While these are true:
(= 1/2 0.5)
(= 1/4 0.25)
This turns out to be false:
(= 1/5 0.2)
I checked the hyperspec, it says that “=” should check for mathematical equivalency despite the types of the arguments. What the heck is going on?
The problem is that 0.2 really is not equal to 1/5. Floating point numbers cannot represent 0.2 correctly, so the literal 0.2 is actually rounded to the nearest representable floating point number (0.200000001 or something like that). After this rounding occurs, the computer has no way of knowing that your number was originally 0.2 and not another nearby non-representable number (such as 0.20000000002).
As for the reason why 1/2 and 1/4 work its because floating point is a base 2 encoding and can accurately represent powers of two.