You're witnessing floating point roundoff error. In short, an infinite range of numbers must be represented in a finite number of bits (specifically, 64 for double precision numbers). The number you're trying to represent doesn't fit perfectly in this system so it's rounded.
Check this out.
x = 39.11237316
% x =
% Even if you round it to 8 dp, it can't be represeneted
% ans =
So, it's not the str2double() that is the problem, it's the finite precision that this number can be represented in.
If higher precision is required you can use symbolic representation for your computations. But the difference between your value and the value being represented is very tiny and usually not a problem.
For a wonderful explanation of floating point roundoff error, see Cleve Moler's article (founder of Matlab).