There's nothing wretchedly wrong with your code that I can see. One this that might make it prettier (and a bit more intuitive) is to park your padding logic in a sub/function similar to the following:

use strict;

while (<DATA>) {
  chomp;
  print padded($_), "\n";
}

sub padded {
  #left-pads enough zeros to a number to ensure that there are at leas
+t
  #four digits
  my ($num) = @_;
  my $padded = '0' x (4 - length($num));
  return $padded . $num;
}

__DATA__
23
102
2003
9
[download]

I am now going to make the obligatory statements about using the -w flag and use strict. There.