Differences between two vectors that suppose to be equal

Does anyone know why those are not all equal?

a=.1:.1:.9; b=[.1 .2 .3 .4 .5 .6 .7 .8 .9];

a==b

     1     1     0     1     1     1     1     1     1

a(3)-b(3)

     5.551115123125783e-17

Answer 1

[dpb]

See the FAQ..

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

[Felipe Arteaga]

From the link above:

The difference is that 0:0.1:0.4 increments by a number very close to but not exactly 0.1 for the reasons mentioned below. So after a few steps it will be off whereas [0 0.1 0.2 0.3 0.4] is forcing the the numbers to their proper value, as accurately as they can be represented anyway.

[Matt Kindig]

To piggyback off this answer, try the following:

format hex
a=.1:.1:.9; b=[.1 .2 .3 .4 .5 .6 .7 .8 .9];
[a', b']

This displays the variable in hex format, which is a representation of the internal binary format that Matlab uses to store the value. Comparing across rows, you can see that the 3rd row differs in the last digit between a and b. Hence the reason a(3) ~= b(3).