Rounding Errors?

In my course, I am told:

Continuous values are represented approximately in memory, and therefore computing with floats involves rounding errors. These are tiny discrepancies in bit patterns; thus the test e==f is unsafe if e and f are floats.

Referring to Java.

Is this true? I've used comparison statements with doubles and floats and have never had rounding issues. Never have I read in a textbook something similar. Surely the virtual machine accounts for this?