subtract two identical float number it gives a very small number not a zero

suposed I have matrix A

A =

    0.9500         0         0
    0.9500         0         0
    0.9500         0         0
    0.9500         0         0
    0.9500         0         0
    0.9500         0         0
    0.9500         0         0
    0.9500         0         0

and I calculate the mean of A as

AA =mean(A)

AA =

    0.9500         0         0

When I do that AA(1,1) - AA(1)

ans =

-1.1102e-16

Why I get this number and not zero ?? Please could you please help?

Answer 1

[Roger Stafford]

Matlab's double precision numbers are in binary form, and therefore cannot represent the quantity 0.9500 exactly. Using binary notation the closest it could come to that number would be:

   .11110011001100110011001100110011001100110011001100110

since it is restricted to a maximum significand (mantissa) of 53 bits. The exact binary expression for 0.9500 would be an infinitely long string analogous to, say, the infinite string for 1/3 in decimal: 1/3 = 0.33333333333333333 ....

When eight such inexact numbers representing 0.9500 are added together one-at-a-time with rounding to 53 bits at each step and the sum divided by 8 the accumulated error is sufficient to show up as a difference in the least significant bit:

   .11110011001100110011001100110011001100110011001100111

That least significant bit has a value of 1.1102e-16, which is what you observed.

Answer 2

[David Young]

It's round-off error. See, for example this question.

Answer 3

[Image Analyst]

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