I\'ve been thoroughly searching for a proper explanation of why this is happening, but still don\'t really understand, so I apologize if this is a repost.
#i
The fix
int k = (int)(j+(j<0?-0.5:0.5));
The logic
You're experiencing a problem with number bases.
Although on-screen, 4.10 is a decimal, after compilation, it gets expressed as a binary floating point number, and .10 doesn't convert exactly into binary, and you end up with 4.099999....
Casting 409.999... to int just drops the digits. If you add 0.5 before casting to int, it effectively rounds to the nearest number, or 410 (409.49 would go to 409.99, cast to 409)