Learn English – “Exact” VS “Accurate” VS “Precise

In a scientific context, accuracy and precision are different things, and some of this difference carries over to these words' non-scientific common usage.

An accurate scientific measurement is one that is very close to the real value. A precise measurement is one that is repeatable with very small variations, whether it's close to the real value or not. An exact scientific value is one that has absolutely zero error: maybe it's a purely defined quantity like the number of centimeters in a meter.

In common usage, accurate describes being close to the correct value. Precise, on the other hand, emphasizes the small margin of error or paying attention to the smallest details. Exact means zero deviation from the correct value.

You should also know that accurate and precise can be applied to either a number or the person generating the number. Exact, on the other hand, is seldom used to describe a person and only describes the number.

Describing a number, say the number of people attending a concert:

I need an accurate count of the people at the concert. [says that you need a number that's close to the truth, but maybe 3,000 is a good enough answer even if it's not exactly correct]

I need a precise count of the people at the concert. [says that you need a number with a small margin of error, something like 2,945 give or take a few]

I need an exact count of the people at the concert. [says that you want a count of every single person with zero error]

Describing an accountant:

She is a very accurate accountant; she has not made a mistake yet. [close to the truth]

She is a very precise accountant; she tracks every cost down to the tenth of a cent. [very small margin of error]

You cannot say "she is a very exact accountant." Exact does not describe people.

There is another adjective, exacting, that is applied to people, but it means "having very high expectations [of others]."

She is a very exacting accountant; she makes me submit receipts for every transaction, no matter how small. [very high expectations]

Looking at your sample sentences:

1. Could be either "precise" (emphasizing "down to the penny") or "exact" (emphasizing "this is the correct value").
2. "Accurate" would be best. You might think "exact" (meaning zero error), but you don't use "exact" to describe people.
3. All three are possible here. I'd probably use "accurate".
4. I'd use "precision" here, in the sense of "attention to the tiniest detail."

Added examples:

1. Either "precise" (meaning "down to the minute or second") or "accurate" (meaning "correct"). "Exact" is fine but sounds less natural.
2. This actually brings up a different shade of meaning. I talked about these three adjectives as modifying a measurement or guess. Here you're using them to modify a real thing that that the speaker is guessing at. In that case, you cannot use the word accurate. You can use either exact (meaning absolutely correct) or precise (meaning known in detail).
3. Same as 2.
4. Same as 2.
5. All three options are possible. "Exact" and "precise" are pretty close synonyms, meaning "identical meanings in both languages." Using "accurate" is a little looser, meaning that there's no word in the other language that comes close to the meaning in English.