I wish to round the float 697.04157958254996 to 10 decimal digits after
the decimal point.

$ python3.0
Python 3.0.1 (r301:69556, Jun  7 2009, 14:51:41)
[GCC 4.3.2 20081105 (Red Hat 4.3.2-7)] on linux2
Type "help", "copyright", "credits" or "license" for more information.

>>> 697.04157958254996
697.04157958254996      # python float can represent this number exactly

>>> 697.04157958250000  # this is the expected result
697.04157958250005      # this is the closest python float representation

>>> round(697.04157958254996, 10)
697.04157958259998      # error

round() gives a result that is closer to
697.0415795826
than the expected result of
697.0415795825
- it has not rounded to the closest 10th decimal digit after the decimal
point.

(python 2.6.2 has the same problem)

Thanks for the report.

This is fixed in Python 3.1 (except on a few unusual hardware/OS 
combinations):

Python 3.1rc1+ (py3k:73252, Jun  6 2009, 10:35:36) 
[GCC 4.0.1 (Apple Computer, Inc. build 5367)] on darwin
Type "help", "copyright", "credits" or "license" for more information.
>>> round(697.04157958254996, 10)
697.0415795825

It's a "won't fix" for Python 2.x.  Rounding to 10 decimal places 
involves multiplying by 10**10., rounding to the nearest integer, then 
dividing by 10**10. again;  the problem in this case is that 
multiplication by 10.**10 is inexact, and the error involved in the 
multiplication by 10**10. pushes the value from the 'round down' region 
into the 'round up region':

Python 2.7a0 (trunk:73252, Jun  6 2009, 10:16:08) 
[GCC 4.0.1 (Apple Computer, Inc. build 5367)] on darwin
Type "help", "copyright", "credits" or "license" for more information.
>>> 697.04157958254996 * 10**10
6970415795825.5
[38623 refs]

There's no easy way to fix this, short of using multiple-precision 
arithmetic to do the rounding (which is what Python 3.1 does).


By the way, Python's float can't represent the number

697.04157958254996

exactly (assuming IEEE 754 arithmetic):  the closest it gets is the 
value:

697.041579582549957194714806973934173583984375

but the repr of a float (in Python 3.0 and 2.x) only produces 17 
significant digits, since that's enough to guarantee that the
repr() value evaluates back to the correct float (assuming correct
rounding).

See also issue 1869 and the issues it links to for additional discussions 
about round.