The result of 0.3+0.15==0.45 is true or false?

Hi, I have a problem. I ran this expression "0.3+0.15==0.45" in Matlab the result is "0", but I ran the same expression in Mathematica, the result is "True". Why is that? AND if a,b are both variables for floating-point numbers, is it acceptable if I use "a==b" as the condition in the "if function"? Could anybody help me out? Thanks a lot!

Answer 1

[Daniel Shub]

You might want to start with the FAQ: http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

[Jan]

And a workaround:

if abs(0.3 + 0.15 - 0.45) < 10*eps

But the limit 10*eps is arbitrary! A relative error would be smarter:

if abs(((0.3 + 0.15) - 0.45) / 0.45) < 10*eps

But if the values are very small, even this might fail.

[Jiasen]

Thanks

[Jan]

@Jiasen: It is a good idea to read the complete FAQ - why not takine advantage from the problems of others...