Though the actual answer (as given by @Per Salmi and @depquid) is just a bit more than 33% (3 bytes become 4, plus line endings, plus some housekeeping) you'll not have to worry about
uuencode dates from the really old days of UNIX, before MIME mailers were around. back in those days, to schlepp bytes around in text only environments (e.g, Mail, netnews/usenet) you'd have to manually encode the file to be 7-bit character safe. Then the receiver would have to manually save the file someplace, possibly concatenate and order multipe mails/postings, run
uudecode (which was smart enough to ignore anything outside of BEGIN/END blocks) and get the binary file. But we don't need to do that anymore, at least not for mail.
If you use any modern mailer, this cross encoding already happens automagicaly. Binary MIME elements are usually base64 encoded (like @depquid states).
So, you already do MIME Base64 encoding, which blows up the file a bit more than 33% if you're curious about the hit to your bandwidth allocation. To do uuencode/uudecode would just add even more work on both yours and the receiver's side.