Python Dictionary Floats

Question

I came across a strange behavior in Python (2.6.1) dictionaries:

The code I have is:

new_item = {'val': 1.4}
print new_item['val']
print new_item

And the result is:

1.4
{'val': 1.3999999999999999}

Why is this? It happens with some numbers, but not others. For example:

0.1 becomes 0.1000...001
0.4 becomes 0.4000...002
0.7 becomes 0.6999...996
1.9 becomes 1.8888...889

Reading this: http://floating-point-gui.de/ may help you understand why. — GWW, Oct 24 '11 at 15:54
possible duplicate of [Floating point inaccuracy examples](http://stackoverflow.com/questions/2100490/floating-point-inaccuracy-examples) - chosen because it was the duplicate cited [in this question](http://stackoverflow.com/questions/2909427/c-floating-point-precision) — Nate, Oct 24 '11 at 15:59
It has nothing to do with the dictionary itself; it has to do with how the dictionary is formatted for display. — Karl Knechtel, Oct 24 '11 at 16:03

Michael Borgwardt · Accepted Answer · 2011-10-24T16:03:51.507

This is not Python-specific, the issue appears with every language that uses binary floating point (which is pretty much every mainstream language).

From the Floating-Point Guide:

Because internally, computers use a format (binary floating-point) that cannot accurately represent a number like 0.1, 0.2 or 0.3 at all.

When the code is compiled or interpreted, your “0.1” is already rounded to the nearest number in that format, which results in a small rounding error even before the calculation happens.

Some values can be exactly represented as binary fraction, and output formatting routines will often display the shortest number that is closer to the actual value than to any other floating-point number, which masks some of the rounding errors.

score 1 · Answer 2 · edited Jun 20 '20 at 09:12

This problem is related to floating point representations in binary, as others have pointed out.

But I thought you might want something that would help you solve your implied problem in Python.

It's unrelated to dictionaries, so if I were you, I would remove that tag.

If you can use a fixed-precision decimal number for your purposes, I would recommend you check out the Python decimal module. From the page (emphaisis mine):

Decimal “is based on a floating-point model which was designed with people in mind, and necessarily has a paramount guiding principle – computers must provide an arithmetic that works in the same way as the arithmetic that people learn at school.” – excerpt from the decimal arithmetic specification.

Decimal numbers can be represented exactly. In contrast, numbers like 1.1 and 2.2 do not have an exact representations in binary floating point. End users typically would not expect 1.1 + 2.2 to display as 3.3000000000000003 as it does with binary floating point.

The exactness carries over into arithmetic. In decimal floating point, 0.1 + 0.1 + 0.1 - 0.3 is exactly equal to zero. In binary floating point, the result is 5.5511151231257827e-017. While near to zero, the differences prevent reliable equality testing and differences can accumulate. For this reason, decimal is preferred in accounting applications which have strict equality invariants.

Python Dictionary Floats

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