python incorrect rounding with floating point numbers

Python 3 rounds according to the IEEE 754 standard, using a round-to-even approach.

If you want to round in a different way then simply implement it by hand:

import math
def my_round(n, ndigits):
    part = n * 10 ** ndigits
    delta = part - int(part)
    # always round "away from 0"
    if delta >= 0.5 or -0.5 < delta <= 0:
        part = math.ceil(part)
    else:
        part = math.floor(part)
    return part / (10 ** ndigits)

Example usage:

In [12]: my_round(0.3125, 3)
Out[12]: 0.313

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Note: in python2 rounding is always away from zero, while in python3 it rounds to even. (see, for example, the difference in the documentation for the round function between 2.7 and 3.3).

If you need accuracy don't use float, use Decimal

>>> from decimal import *
>>> d = Decimal(0.3125)
>>> getcontext().rounding = ROUND_UP
>>> round(d, 3)
Decimal('0.313')

or even Fraction