Here is an easy example to see if your mathematical software deals with floating point correctly.
You want to divide two thirds by five sixths. So you use GNU bc
stany@Gilva:~[11:13 PM]$ echo "(2/3) / (5/6)" | bc -l .79999999999999999999 stany@Gilva:~[11:14 PM]$
Matlab, which is arguably better at math then bc is, gives me this:
EDU>> (2/3) / (5/6)
ans =
0.8000
EDU>>
2*6 / 3*5 = 12/15 = 4/5 = 0.8 so Matlab is correct, and bc is wrong.