Floating point arithmetic is not commutative.
You can see the effect with even simple calculations
format long g
example = 29/7*7
fprintf('%.999g\n', example)
example - 29
Remember that binary floating point does not use decimal internally.
Using decimal would not solve the problems: consider that in decimal, to 10 decimal places
1/3 == 0.3333333333
0.3333333333 * 3 = 0.9999999999
1 - 0.9999999999 = 0.0000000001
Every finite-representation number base has the same problem when it comes to dividing by a value that is relatively prime to the base. Base 60 arithmetic, for example, would be happy with fractions 1/2, 1/3, 1/4, 1/5, 1/6, 1/10, 1/12 -- but would have the same kind of problems for 1/7 .
