Actually, this is going a bit off topic, since it doesn't especially matter to me whether exact integers are a subset of inexact numbers. I thought I even deleted this part of my reply, but oh well. XD
Looks like the racket docs say[1] Racket's inexact numbers are IEEE floating-point numbers of single or double precision, with double being the default. So they don't preserve integers beyond 53 bits:
Odd, this suggests Racket double-precision floating-point numbers have only 51 bits of mantissa rather than 52, so maybe they actually only preserve integers up to 52 bits...?
I "solved" this issue by simply making all numbers 64-bit floating point. The change was really easy to make. I didn't do it because of this issue, though. I did it because I want to eventually compile to JS, and JS only has 64-bit floating point.
Though, it also makes it easier conceptually to only have to worry about floating point, as compared to floating point + integer + rational + complex + whatever else Racket has. Even if you divide numbers into exact/inexact like Racket does, that's still more complicated than only having a single numeric type.