Why doesn't .3 - .2 - .1 = 0

I was bored yesterday at work and I was playing around with some decimal numbers when I stumbled across something I thought was pretty interesting.

.3 - .2 - .1 != 0

but

.2 - .1 - .1 = 0

then I began to run some other tests and I found out that only .3 and .8 are the only numbers that you use that'll not get you a 0 answer. If you take:

.4 - .2 - .1 - .1 = 0

and

.9 -.2 -.1 -.1 -.1 -.2 -.1 -.1 = 0

If you change any of the .2's to two - .1's you don't get 0. So what’s so special about those 2 decimals that make them the only ones that don't work with basic subtraction?

Answer 1

[Matt J]

What makes them special? Nothing. There are lots more numbers like that

    >> isequal(0, .7 - .5 - .2)

    ans =

         0

It also depends on the operation you do. Sometimes 0.3 will work fine, e.g.,

    >> isequal(0, .6 - .3 -.3)

    ans =

         1

[Matt Fig]

It is not just in MATLAB. ALL numerical systems that follow IEEE 754 will behave this way. That is the standard.

[José-Luis]

This is not Matlab specific. It has to do with the fact that computers use binary numbers and humans tend to feel more comfortable with decimals. Things gets lost in translation and these are the side effects.

Answer 2

[Thomas]

This should answer your question. Look at the wiki under the section Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero? (might have to scroll on the page to locate...)

http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

[Dr. Seis]

I had similar issues when doing mod(0.4,0.4) and mod(0.8,0.4) returning a number slightly smaller than 0.4 instead of 0. Whenever I do these types of comparisons in the future I will need to overload the builtin functions.

See this for example: http://www.mathworks.com/matlabcentral/answers/49910-mod-bug-or-something-else

[Oleg Komarov]

@Lucas, if you already know that you wouldn't be asking the question in the first place. I recommend to read the FAQ more carefully.