This is actually a really great teaching moment as floating point unreliability extends beyond just python. For example, the number .1 seems like an awful easy number to represent, right? It's just one tenth. Unfortunately, the computer doesn't work in base 10, but base 2, and in base 2, .1 is an irrational number (a number that repeats on and on for infinity, like 1/3 is .33333333333).

This actually ties back swimmingly to our discussion of the posterior distribution. Every time we work with floating point, we slightly reduce our confidence. For example, if we write the code

foo=1.0
foo=foo/10
foo=foo*10

then foo is actually just a hair off from 1.0. Python's pretty smart and can figure out that rounding error in most cases, but if it didn't automatically correct for us and we kept running the last 2 lines over and over again, we'd slowly be less and less able to say we were confidently at 1.0, but could only say we were close to it.

Now think about that in the context of the robot moving from the imprecise movement lesson. Every time the robot moves, it's fairly confident it knows where it moved, but it could be a little to the left or a little to the right. The more it moves, the less confident it's actually where it expects.

If you want to delve deeper into the topic, there's an MSDN article talking about the imprecision of floating point Here. I know this is a little deeper than the question you asked, but it's really interesting, especially the way it ties back so perfectly with the class, so I thought I'd share that neat little tidbit.

If anyone wishes to read into this a bit deeper, I highly recommend this paper:

What Every Computer Scientist Should Know About Floating-Point Arithmetic

For an excellent discussion about floating point numbers and these weird rounding errors, check out this lecture from MIT's introductory programming class. Start at 5:40 to get to the relevant part.

Thanks for asking this question many students may be wondering why this occurs, well worth reading. Maybe add a link back to this question from Course web page? I bet It will get used. Consider adding links for 10 most popular answers.

MrSparc,

I just checked g++. (SEE EDIT BELOW, this code originally compared 1/5==2 rather than .2 :( )

int main()
{
   //volatile is used to try and prevent optimizations. Let me know if this doesn't actually work
   //but the assembler seems to indicate the code does the right thing.
   volatile double a = 1.0;
   volatile double b = 5.0;
   volatile double c = 0.2;
   if(a/b == c){
       printf("Python is weird\n");
   }else{
       printf("Floating point is weird\n");
   }
}

The first

EDIT: The above code was completely wrong because I dyslexically swapped 0.2 with 2.0. The first is given ("Python is weird"), but as a commenter below pointed out, there are potentially optimization issues going on here. I'm going to check the assembler to see what's going on.