Get as close to pi as you can
C++ 158 chars
#include&lt;iostream&gt;
#include&lt;iomanip&gt;
int main(){double p=0;for(long long l=1;l&gt;0;l+=2){p+=(double)4/l;l+=2;p-=(double)4/l;}std::cout&lt;&lt;std::setprecision(30)&lt;&lt;p;}

Simply calculates pi by brute force until my computer can't store the number to divide 4 by.
I got to 3.1415926535792384 before I killed it. The highlighted part is what is off; it should have been 3.1415926535897932.  Eventually, it would have got there.