[docs] [issue14245] float rounding examples in FAQ are outdated

Sat Mar 10 12:26:28 CET 2012

Mark Dickinson <dickinsm at gmail.com> added the comment:
Proposed rewrite:
Why are floating point calculations inaccurate?
-----------------------------------------------
Users are often surprised by results like this::
 >>> 1.2 - 1.0
 0.199999999999999996
and think it is a bug in Python. It's not. This has little to do with Python,
and much more to do with how the underlying platform handles floating-point
numbers.
Python floats are stored internally in binary floating-point, using a fixed
precision (typically 53 bits). Many numbers that can be written easily in
decimal notation (``1.2``, for example), cannot be expressed exactly in this
internal binary format. After::
 >>> x = 1.2
the value stored for x is a (very good) approximation to the value ``1.2``, but
is not exactly equal to it. (On a typical machine, the actual stored value
is::
 1.1999999999999999555910790149937383830547332763671875
which is accurate to around 16 decimal digits.) Similarly, the result of any
floating-point operation must often be rounded to fit into the internal format,
resulting in another tiny error.
For a more detailed explanation of what's involved, please see the chapter on
:ref:`floating point arithmetic <tut-fp-issues>` in the Python tutorial.

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