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Python Python Basics (2015) Python Data Types Numbers

Posted by A X
A X
12,842 Points

Why does 0.1 + 0.1 + 0.1 - 0.3 = 5.5...-e17 (really long scientific notation) in Python?

Hi all, Just starting to dip into Python, and I'm really curious to understand what's going on in "Python logic" that when we do a simple seeming math problem that should return 0 (like 0.1 + 0.1 + 0.1 - 0.3 should equal 0) we get scientific notation instead. It seems like there's other times when Python interprets math problems differently from what we'd expect. Why is this?

*Also please explain your answer in simplistic terms please, I'm still a beginner

3 Answers

jcorum
jcorum
71,830 Points
jcorum
jcorum
71,830 Points

This isn't anything to do especially with Python. It occurs in all programming languages. And in math.

In decimal arithmetic if we add 1/4 + 1/4 + 1/4 + 1/4 we get 1.00, exactly. And if we add 1/3 + 1/3 + 1/3 we get 1.00 as the total. If we add 0.25 + 0.25 + 0.25 + 0.25 we also get 1.00. But if we add 0.333 + 0.333 + 0.333 we don't. We get a close approximation: 0.999. And it doesn't matter how many decimal places you go out to (0.3333333, or 0.33333333333333), you'll never get to 1.00. Some decimal fractions are "different", they go on forever.

The same is true in binary arithmetic. Some binary decimal fractions are also "different". Because they are finite representations of repeating decimals, they are approximations, just as 0.333 is an approximation of 1/3.

So, when you add them together, the result may not come out exactly as expected.

docgunthrop
docgunthrop
12,445 Points

I get what you're saying, but in the example, 0.1 and 0.3 do not have repeating decimals.

sethchristiansen
sethchristiansen
2,379 Points
sethchristiansen
sethchristiansen
2,379 Points

The thought process that the answer should equal zero comes from using the base 10 system. Python uses base 2 (binary). In this case, the number .1 in base 10 cannot be represented precisely in base 2, only approximately.

More can be found about this in the Python documentation: https://docs.python.org/2/tutorial/floatingpoint.html

jcorum
jcorum
71,830 Points
jcorum
jcorum
71,830 Points

nekilof, you are right. They don't in decimal. But at least one of them does in binary.