PI and accuracy of a floating-point number

Question

A single/double/extended-precision floating-point representation of Pi is accurate up to how many decimal places?

Answer 1

#include <stdio.h>

#define E_PI 3.1415926535897932384626433832795028841971693993751058209749445923078164062

int main(int argc, char** argv)
{
    long double pild = E_PI;
    double pid = pild;
    float pif = pid;
    printf("%s\n%1.80f\n%1.80f\n%1.80Lf\n",
    "3.14159265358979323846264338327950288419716939937510582097494459230781640628620899",
    pif, pid, pild);
    return 0;
}

Results:

[quassnoi #] gcc --version
gcc (GCC) 4.3.2 20081105 (Red Hat 4.3.2-7)

[quassnoi #] ./test

3.14159265358979323846264338327950288419716939937510582097494459230781640628620899

3.14159274101257324218750000000000000000000000000000000000000000000000000000000000
        ^
3.14159265358979311599796346854418516159057617187500000000000000000000000000000000
                 ^
3.14159265358979311599796346854418516159057617187500000000000000000000000000000000
                 ^
  0000000001111111
  1234567890123456