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I was under the impression that tert-butyl would be refered to as 2-methylpropyl not 2,2-dimethylpropyl. 2,2-dimethylpropyl would be a chain of 3 carbons with 2 methyl groups at the 2 position. You would have to name it 1,1-dimethyl-ethyl, but that isn't correct either because you now are no longer selecting the longest chain which is the first step in getting the base name of the group/compound of interest usually. 2,2-dimethylpropyl would be the compound C(CH3)4 which isn't what we have. We have -C(CH3)3. I could be wrong since I am a few years removed from my naming practice, but this is correct.