Python: Why does .1 + .1 + .1 - .3 not equal 0?

Question

Edit: I am aware this question was already answered, I just didn't find it. Thanks to everyone who pointed me in the right direction.

Why is it that when I run the following code the answers are not 0?

a = .1
d = .3

x = - a - a - a + d
y = a + a + a - d

print(f'x is {x}')
print(f'x is {y}')

In other words -.1 - .1 - .1 + .3 and .1 + .1 + .1 - .3

Instead I get the following:

x is -5.551115123125783e-17
y is 5.551115123125783e-17

It's almost zero but it isn't zero.

Is this due to how the python language works, is it a hardware thing, or something else?

I can't seem to find anything on stack overflow concerning this and would really like to understand what is going on.

[Floating point arithmetic](https://floating-point-gui.de/) – it's-yer-boy-chet Aug 01 '18 at 17:59 — it's-yer-boy-chet, Aug 01 '18 at 17:59
ok thanks ill check there, marked my post as a duplicate – Alex Lussier Aug 01 '18 at 18:02 — Alex Lussier, Aug 01 '18 at 18:02

score 3 · Accepted Answer · edited Aug 01 '18 at 18:23

3

See this article: David Goldberg - What Every Computer Scientist Should Know About Floating-Point Arithmetic

Essentially, this is a well known issue with floating point arithmetic. You could use the round function, and round to a very small digit for practical precision.

round(-5.551115123125783e-17, 10) will still return 0, which is what you want.

edited Aug 01 '18 at 18:23

joelhed

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answered Aug 01 '18 at 18:03

Rohan Singh

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Thanks for the article, will definitely be reading that – Alex Lussier Aug 01 '18 at 19:19

score 0 · Answer 2 · answered Aug 01 '18 at 18:02

This is due to the way most programming languages store floating point numbers, where .1 + .1 + .3 would equal 0.30000000000000004.

Instead of checking if it's 0, try just checking if the absolute value of the different between them is smaller than a certain number:

abs((.1+.1+.3)-.3) < 0.0001

Python: Why does .1 + .1 + .1 - .3 not equal 0?

2 Answers2