You could use Regexp::Common's "number" extension to detect reals, which is what you seem to be seeking:

if( $string =~ /^$RE{num}{real}$/ ) {
  print "Match!\n";
}
else {
  print "Reject!\n";
}
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You don't want to invent this yourself. Just look at the regular expression that $RE{num}{real} contains:

perl -MRegexp::Common=number -E 'say $RE{num}{real}'
(?:(?i)(?:[-+]?)(?:(?=[.]?[0123456789])(?:[0123456789]*)(?:(?:[.])(?:[
+0123456789]{0,}))?)(?:(?:[E])(?:(?:[-+]?)(?:[0123456789]+))|))
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...better off using a solution from Regexp::Common, or the looks_like_number() utility Limbic~Region suggested, or both.