Error in ceil() function?

Hello,

Does anybody know why the ceil()-function Returns two different values in the following case?

X=[4 (1-0.95)*80]; ceil(X)

ans =

     4     5

Thank you!

Answer 1

[Stephen23]

Floating point numbers are how decimal values are stored in your computer: they do not have infinite precision, and they can only approximate many values. Even if it looks like the "actual" value is being shown to you this does not mean that the internal representation inside your computer is the same value.

Lets have a quick look at those values:

>> X=[4 (1-0.95)*80]
X =
   4.0000   4.0000
>> fprintf('%.30f\n',X)
4.000000000000000000000000000000
4.000000000000003552713678800501

It is not a problem with MATLAB, this is simply how (binary) computers work.

Read all about it:

http://de.mathworks.com/matlabcentral/answers/69-why-does-1-2-3-1-3-not-equal-zero

http://de.mathworks.com/matlabcentral/answers/57444-faq-why-is-0-3-0-2-0-1-not-equal-to-zero

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

And if you want to see what the decimal equivalent of a floating point value is, then try this FEX submission:

http://www.mathworks.com/matlabcentral/fileexchange/22239-num2strexact--exact-version-of-num2str-

As its author points out: "Don't confuse the exact conversion with significance!"