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 a     c      a+c
--- + --- => -----
 b     d      b+d

a/b = 0/1
c/d = 1/0 [This is infinity, larger than any number]

frac(3.14159265358979);
sub frac
...
    ($e,$f) = ($a+$c, $b+$d);
    print "$a/$b < $x < $c/$d; => $e/$f\n";
} }

1/1 < 3.14159265358979 < 1/0; => 2/1
2/1 < 3.14159265358979 < 1/0; => 3/1
...
2108/671 < 3.14159265358979 < 355/113; => 2463/784
2463/784 < 3.14159265358979 < 355/113; => 2818/897
2818/897 < 3.14159265358979 < 355/113; => 3173/1010