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

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