Why I got x=0.15000000000000002 during adding 0.050 in each step using while lopp in python

Question

I run the below python code,

x=0
while x<1:
    x+=0.050
    print(x)

and got the following result. Which I don't understand.

0.05 0.1 0.15000000000000002 0.2 0.25 0.3 0.35 0.39999999999999997 0.44999999999999996 0.49999999999999994 0.5499999999999999 0.6 0.65 0.7000000000000001 0.7500000000000001 0.8000000000000002 0.8500000000000002 0.9000000000000002 0.9500000000000003 1.0000000000000002

https://docs.python.org/3/library/decimal.html, use decimal and read for binary representation problems in computing, you can use google — Vitaliy Terziev, Apr 06 '19 at 18:02
related: [Is floating point math broken?](https://stackoverflow.com/questions/588004/is-floating-point-math-broken) — kmdreko, Apr 06 '19 at 18:02
Check this out too: https://docs.python.org/3/tutorial/floatingpoint.html — Devesh Kumar Singh, Apr 06 '19 at 18:04

score 1 · Answer 1 · answered Apr 06 '19 at 18:16

You are doing floating point calculations, and I think this is the first time you see a floating point error. This error is not dependant on Python but on the underlying implementation of a real number in the computer: unfortunately, many real numbers cannot be represented perfectly inside the machine since the memory can only handle a finite number of digits, so it truncates the number, effectively committing an error.

"But 0.05 doesn't have infinite digits", you will say. This would be true if computers worked in base 10, but they use base 2 - binary - numbers, so what has a finite digit representation in base 10 might have a periodic representation in binary.

For the sake of your program, you might as well reduce the precision of the numbers printed, since the error won't be noticeable in the scope of your problem (the error doesn't accumulate that much), in this way:

print("{.3f}".format(x))

I suggest looking it up on Google and visiting the links in other comments, it's a very interesting topic.

Since you make mistakes while doing this kind of calculations, absolutely avoid using float types when doing important stuff, such as monetary contability! You should use an arbitrary precision type instead, like Decimal.

Why I got x=0.15000000000000002 during adding 0.050 in each step using while lopp in python

1 Answers1