This could help you get started:

use warnings;
use strict;

while (<DATA>) {
  chomp;
  my $data = $_;
  print "$data: ";
  my $result = ($data =~ /^[+\-]?\$?[0-9.]+$/) ? 
    "numeric" : "non-numeric";
  print "$result\n";
}
__DATA__
1020
$10.21
-1023
+1.024
beer
10$25
-$102.6
A1027
1028$
$
$-1.029
[download]

BTW, watch out for those asterisk opertors in your patters. You used \d*, and the '*' could legitimately match '', since it does match a digit zero or more times! That pesky asterisk operator can lead to 'zero-width' matches, which can drive you nuts when you are starting with regular expresssions.