So I know about floating point precision (and how things like 1.1 can't be expressed exactly in binary) and all that, but I'm wondering: how then, do math-related libraries implement infinite precision? In other words, how would you represent, for example, 1.1 accurately in binary? Just a brief description would be great, I can figure out the exact details myself. Thanks. :)
There are no infinite precision libraries, but there are arbitrary precision libraries. For details of how these are implemented, read some documentation :-)
To represent 1.1 exactly in binary, floating point can't be used as you correctly point out. It can be represented if you store the integral part (1) as an integer, and the fractional part (.1) as another integer, and then you need to create the logic to deal with these structures. Alternatively, it could be stored as a fraction (11/10) with both the denominator and the numerator stored as integers.