Why is Python's round so strange?

Question

My code:

  #!/usr/bin/python
  # -*- coding: utf-8 -*-
  print (round(1.555, 1))  # It seems normal
  print (round(1.555, 2))  # Why it is not output 1.56?
  print (round(1.556, 2))  # It seems normal

Output:

  sam@sam:~/code/python$ ./t2.py
  1.6
  1.55
  1.56
  sam@sam:~/code/python$

round(1.555, 1) outputs 1.6.

Why doesn’t round(1.555, 2) output 1.56?

Asked By: sam

||

Source

Answer 1

Straight from the documentation:

The behavior of round() for floats can be surprising: for example,
round(2.675, 2) gives 2.67 instead of the expected 2.68. This is not a
bug: it’s a result of the fact that most decimal fractions can’t be
represented exactly as a float. See Floating Point Arithmetic: Issues
and Limitations for more information.

Answered By: Hunter McMillen

Answer 2

From http://docs.python.org/2/library/functions.html#round:

Note

The behavior of round() for floats can be surprising: for example, round(2.675, 2) gives 2.67 instead of the expected 2.68. This is not a bug: it’s a result of the fact that most decimal fractions can’t be represented exactly as a float. See Floating Point Arithmetic: Issues and Limitations for more information.

Answered By: Adrián

Answer 3

Take a look at the documentation:

Note The behavior of round() for floats can be surprising: for example, round(2.675, 2) gives 2.67 instead of the expected
2.68. This is not a bug: it’s a result of the fact that most decimal
fractions can’t be represented exactly as a float. See Floating
Point Arithmetic: Issues and Limitations for more information.

If you keep digging (i.e. click that link), you’ll find an example similar to yours:

The documentation for the built-in round() function says that it
rounds to the nearest value, rounding ties away from zero. Since the
decimal fraction 2.675 is exactly halfway between 2.67 and 2.68,
you might expect the result here to be (a binary approximation to)
2.68. It’s not, because when the decimal string 2.675 is converted
to a binary floating-point number, it’s again replaced with a binary
approximation, whose exact value is
2.67499999999999982236431605997495353221893310546875

String formatting won’t fix your problem either. The floating point number just isn’t stored the way you’d expect it to be:

>>> '{:0.2f}'.format(1.555)
'1.55'

This isn’t really a “fix”, but Python does have a decimal module, which is designed for floating point arithmetic:

>>> from decimal import Decimal
>>> n = Decimal('1.555')
>>> round(n, 2)
Decimal('1.56')

Answered By: Blender

Answer 4

Using ROUND_CEILING decimal:

>>> from decimal import Decimal, ROUND_CEILING, ROUND_FLOOR
>>> Decimal(1.555).quantize(Decimal('0.01'), rounding=ROUND_CEILING)
> Decimal('1.56')
>>> Decimal(2.675).quantize(Decimal('0.01'), rounding=ROUND_CEILING)
> Decimal('2.68')
>>> Decimal(2.665).quantize(Decimal('0.01'), rounding=ROUND_FLOOR)
> Decimal('2.66')

Answered By: Criscach Cachaña

Why is Python's round so strange?

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