Movement in 2D games (round position when blinking?)

I am using Python 2.x and Pygame for playing with codes. Pygame has an inline rectangle that only supports ints instead of floats. So I created my own rect class (MyRect) that supports floats. Now my question is this:

2D platformer char moves its position (x, y -> both floats). Now when I hit a char to the screen, is the position rounded to int (int (round (x))) or just converted to int (int (x))? I know this might sound a little silly, but I have a problem with this and would like to know how this is usually handled.