if( $string =~ /^$RE{num}{real}$/ ) {
  print "Match!\n";
}
else {
  print "Reject!\n";
}

##</code><code>##

perl -MRegexp::Common=number -E 'say $RE{num}{real}'
(?:(?i)(?:[-+]?)(?:(?=[.]?[0123456789])(?:[0123456789]*)(?:(?:[.])(?:[0123456789]{0,}))?)(?:(?:[E])(?:(?:[-+]?)(?:[0123456789]+))|))