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Phrase(s): hang by a hair [and] hang by a thread
1. Lit. to hang by something very thin, such as a thread or a hair. • The tiniest part of the mobile hung by a thread, the rest are on plastic cords. 2. and hang on by a hair; hang on by a thread Fig. to depend on something very insubstantial; to hang in the balance. • Your whole argument is hanging by a thread. • John isn’t failing geometry, but his passing grade is just hanging by a hair.
McGrawhill's American Idioms And Phrasal Verbs