This is an alternate version of blazar's solution, which may be slightly easier for new Perl programmers (and possibly future maintenance programmers) to understand:

#my $date = "$mon/$mday/$year";
my $date = "10/13/2006";
my ($mon,$mday,$year) = split('/',$date);
$mon = sprintf("%02d",$mon);
$mday = sprintf("%02d",$mday);
$date = "$mon/$mday/$year";
[download]

Also, I'd like to point the OP to Date::Calc and Date::Format.