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Phrase(s): come (a)round
1. finally to agree or consent (to something). • I thought he’d never agree, but in the end he came around. • She came round only after we argued for an hour. 2. to return to consciousness; to wake up. • He came around after we threw cold water in his face. • The boxer was knocked out, but came round in a few seconds.
McGrawhill's American Idioms And Phrasal Verbs