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B. Floating Point Arithmetic: Issues and Limitations http://www.vithon.org/tutorial/2.5/node16.html

0.0001100110011001100110011001100110011001100110011...

Stop at any finite number of bits, and you get an approximation. This is why
you see things like:

>>> 0.1
0.10000000000000001

On most machines today, that is what you'll see if you enter 0.1 at a Python
prompt. You may not, though, because the number of bits used by the
hardware to store floating-point values can vary across machines, and Python
only prints a decimal approximation to the true decimal value of the binary
approximation stored by the machine. On most machines, if Python were to
print the true decimal value of the binary approximation stored for 0.1, it
would have to display

>>> 0.1
0.1000000000000000055511151231257827021181583404541015625

instead! The Python prompt uses the builtin repr() function to obtain a
string version of everything it displays. For floats, repr(float) rounds the true
decimal value to 17 significant digits, giving

0.10000000000000001

repr(float) produces 17 significant digits because it turns out that's enough
(on most machines) so that eval(repr(x)) == x exactly for all finite floats x,
but rounding to 16 digits is not enough to make that true.

Note that this is in the very nature of binary floating-point: this is not a bug
in Python, and it is not a bug in your code either. You'll see the same kind of
thing in all languages that support your hardware's floating-point arithmetic
(although some languages may not display the difference by default, or in all
output modes).

Python's builtin str() function produces only 12 significant digits, and you
may wish to use that instead. It's unusual for eval(str(x)) to reproduce x,
but the output may be more pleasant to look at:

>>> print str(0.1)
0.1

It's important to realize that this is, in a real sense, an illusion: the value in
the machine is not exactly 1/10, you're simply rounding the display of the
true machine value.

Other surprises follow from this one. For example, after seeing

>>> 0.1
0.10000000000000001

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