Exact means correct in every detail. For example, an exact copy is the same in every detail as the thing it is copied from. I don't remember the exact words The exact number of protest calls has not been revealed It's an exact copy of the one which was found in Ann Alice's room. = precise approximate + exactly ex·act·ly Try to locate exactly where the smells are entering the room Both drugs will be exactly the same Barton couldn't remember exactly. = precisely approximately
If something exacts a high price, it has a bad effect on a person or situation. The sheer physical effort had exacted a heavy price The strain of a violent ground campaign will exact a toll on troops. see also exactly
When someone exacts something, they demand and obtain it from another person, especially because they are in a superior or more powerful position. Already he has exacted a written apology from the chairman of the commission
To demand or require authoritatively or peremptorily, as a right; to enforce the payment of, or a yielding of; to compel to yield or to furnish; hence, to wrest, as a fee or reward when none is due; followed by from or of before the one subjected to exaction; as, to exact tribute, fees, obedience, etc
marked by strict and particular and complete accordance with fact; "an exact mind"; "an exact copy"; "hit the exact center of the target
You say to be exact to indicate that you are slightly correcting or giving more detailed information about what you have been saying. A small number -- five, to be exact -- have been bad