An alternate way of doing this might be to break out your MM/DD/YYYY into seperate chunks (ie $MM = month, $DD = day, and $YYYY = year), then take the day variable and add zero to it. Then put it all back together again. This way you could manipulate the date if you needed to.
($MM, $DD, $YYYY) = split(/,"$date");
$MM=$MM+0;
$DD=$DD+0;
$date=$MM."/".$DD."/".$YYYY;
Please forgive me if my split syntax is incorrect. I don't have an example in front of me. Anyway, I am just providing an alternate methodry. Although if you absolutely need to use a regex or want to get better at using them, this definitely won't help you!
Have fun!
UPDATE: Thanks flounder99 for the correction, I thought that I was missing something!