"precise, rigorous, accurate," 1530s, from Latin exactus "precise, accurate, highly finished," past participle adjective from exigere "demand, require, enforce," literally "to drive or force out," also "finish, measure," from ex- "out" (see ex-) + agere "drive, lead, act" (see act, n.).

mid-15c., from Latin exactus, past participle of exigere "require, enforce, demand, collect (money);" see exact, adj.. Older in English than the adjective and retaining the literal sense of the Latin source. Related: Exacted; exacting.