I have gone into Preferences > Advanced > Importing and selected the MP3 option but the songs are still downloading as MP4 files. When I try the Burn to MP3 CD option, I receive a message stating these files can't be converted to MP3.
Tracks you purchase from the iTunes store are in protected AAC format M4P and can't be converted. The preference you are setting has nothing to do with downloading from the store, it sets the format for importing tracks from your CDs: About the Add to Library, Import and Convert functions
As the other reader stated you cannot adjust the download setting for the iTunes Store, only other sources. It actually says this in very small print in Preferences/advanced/importing dialog box at the very bottom. If AAC files can never be changed, maybe we should consider other download sources (eg: Limewire,free!). What I have done in the past was to burn the AAC files to disc and then upload them to a non-iTunes jukebox in mp3 format. Not fun as you have to manually insert titles and names.
If you are ripping from CD, I would strongly suggest using Exact Audio Copy (EAC) and LAME. I think both can be downloaded from download.com. They work very well and produce what I think is the highest quality mp3's you can get (at least with free software and maybe even pay software).
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How come my songs download as MP4 instead of MP3?
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