Personally, I'd put much more faith in theDamian and Abigail's code than my own. I'd use Regexp::Common.

use Regexp::Common qw /number/;

for ('1', 'flip', '-2.3e14', '0.01', 'flop') {

    /$RE{num}{real}/ and print "Yup, $_ is a number!\n";

}
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-Bird