Actually you don't need to worry how big is big at all, just let Perl do everything for you.

Here is a piece of code I come up with:

use Data::Dumper;

$str = $ARGV[0];
$a = $str + 0.0;
if ($a =~ m/INF/) {
    use bignum;
    $a = $str + 0.0;
    no bignum;
}

print Dumper($a);
[download]

Play with it like this:

perl -w test.pl 9e5000, will give you a BigInt
perl -w 12.3, will give you a normal guy

With limited testing, I cannot promise that it will work for all the situations, so try it out.