Etymology
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Words related to exact

ex- 
word-forming element, in English meaning usually "out of, from," but also "upwards, completely, deprive of, without," and "former;" from Latin ex "out of, from within; from which time, since; according to; in regard to," from PIE *eghs "out" (source also of Gaulish ex-, Old Irish ess-, Old Church Slavonic izu, Russian iz). In some cases also from Greek cognate ex, ek. PIE *eghs had comparative form *eks-tero and superlative *eks-t(e)r-emo-. Often reduced to e- before -b-, -d-, -g-, consonantal -i-, -l-, -m-, -n-, -v- (as in elude, emerge, evaporate, etc.).
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*ag- 

Proto-Indo-European root meaning "to drive, draw out or forth, move."

It forms all or part of: act; action; active; actor; actual; actuary; actuate; agency; agenda; agent; agile; agitation; agony; ambagious; ambassador; ambiguous; anagogical; antagonize; apagoge; assay; Auriga; auto-da-fe; axiom; cache; castigate; coagulate; cogent; cogitation; counteract; demagogue; embassy; epact; essay; exact; exacta; examine; exigency; exiguous; fumigation; glucagon; hypnagogic; interact; intransigent; isagoge; litigate; litigation; mitigate; mystagogue; navigate; objurgate; pedagogue; plutogogue; prodigal; protagonist; purge; react; redact; retroactive; squat; strategy; synagogue; transact; transaction; variegate.

It is the hypothetical source of/evidence for its existence is provided by: Greek agein "to lead, guide, drive, carry off," agon "assembly, contest in the games," agōgos "leader," axios "worth, worthy, weighing as much;" Sanskrit ajati "drives," ajirah "moving, active;" Latin actus "a doing; a driving, impulse, a setting in motion; a part in a play;" agere "to set in motion, drive, drive forward," hence "to do, perform," agilis "nimble, quick;" Old Norse aka "to drive;" Middle Irish ag "battle."

exacting (adj.)
"very demanding, severe in requirement," 1580s, present-participle adjective from exact (v.).
exacta (n.)
type of horse-racing bet involving picking the first two horses in a race in order of finish, 1964, said to have originated in New York; from exact (adj.).
exaction (n.)

late 14c., exaccioun, "action of demanding payment; imposition, requisitioning" of taxes, etc., from Old French exaccion and directly from Latin exactionem (nominative exactio) "a driving out; supervision; exaction; a tax, tribute, impost," noun of action from past-participle stem of exigere (see exact (adj.)). Meaning "a tax, tribute, toll, fee," etc. is from mid-15c.

exactitude (n.)

"quality of being exact, accuracy, particularity," 1734, from French exactitude (17c.), from exact, from Latin exactus (see exact (adj.)).

exactly (adv.)

"in an exact manner, with minute correctness," 1530s, from exact (adj.) + -ly (2). Elliptical use for "quite right" not recorded before 1869.

exactness (n.)
1560s, "perfection," from exact (adj.) + -ness. Meaning "precision" is 1640s.
inexact (adj.)
1791, from in- (1) "not, opposite of" + exact (adj.). Perhaps modeled on French inexact (18c.). Related: Inexactly.