Why does this algorithm yield an 'incorrect' result?

The following code yields cumul_total = 2.000000000026658e+05 . What is the '26658' on the end? Why does this occur?

Thank you

A = (0.2);
cumul_total = (0.0);

for iii = 1:1e6
    cumul_total = cumul_total + A;
end

cumul_total

Answer 1

[DGM]

This is a consequence of accumulating the small errors inherent to floating-point representations of numbers.

A = 0.2;
S = 0;

% watch the error
format long
for k = 1:100
    S = S+A
end

Note the remarks on accuracy and pitfalls here.

https://www.mathworks.com/help/matlab/matlab_prog/floating-point-numbers.html#f2-98690