"Exact" VS "Accurate" VS "Precise

Question

Exact: (synonym : Precise)
in great detail, or complete, correct, or true in every way.

Precise:
exact and accurate.

The bunker's precise location is a closely guarded secret.

Accurate:
correct, exact, and without any mistakes.

My researches' gist:

Based on my search, exact amount/location/thing is the most detail-oreinted and the most correct one, an accurate amount/location/thing is a less exact, but still too close to the true and the precise... is the least true one but with a very small standard deviation (at least scientifically and when it comes to aiming and target or the weight of something with decimal numbers etc.)

Some people believe that they are interchangeable in everyday speech without any difference in meaning, some other divide them scientifically. [Source]

But there are some other sources that claim something else! Like:

In scientific contexts, though, "exact" and "accurate" may have different meanings. For example, the ratio of the circumference of a circle to its diameter is exactly equal to pi=3,1415...

R=3,14 is an accurate approximation of that ratio, to within 0,01.

Accurate: with small error; exact: with no error. [Source] {Based on this part, I think "precise" is something with more error than "accurate".}

Now, I wonder what word fits the best for each case below and why:

1 - I still owe you £7, don't I?" "Actually, it's £7.30 to be .........."

a. exact
b. accurate
c. precise

2 - He is a very ........... accountant. He makes no mistakes at all.

a. exact
b. accurate
c. precise

3 - This is a .............. machine. It works without any error.

a. exact
b. accurate
c. precise

4 - He's a very careful person. He always performa his tasks with high...................

a. exactness
b. accuracy
c. precision

Bringing up this question, I was going to discover the nuance between these quite similar words and find out where and when can I use each one?

Added examples:

1. a. Can you tell me the ...... time?
   b. Yes, it's 4:26.
   

a. exact
b. precise
c. accurate

2. I forgot the ........ age difference between them, but I think they're two or three years apart.

a. exact
b. precise
c. accurate

3. a. Try to remember his ........ words. It's very inportant for us to make a decision.

a. exact
b. precise
c. accurate

4. Can you remember her bitthday's ......... date?

a. exact
b. precise
c. accurate

5. Some English words may have no ............ equivalents in another language.

a. exact
b. precise
c. accurate

Some resources that I have studied:

http://www.softschools.com/difference/precise_vs_accurate/34/

https://forum.wordreference.com/threads/exact-vs-accurate.72978/

https://www.google.com/amp/s/www.differencebetween.com/difference-between-exact-and-vs-accurate/amp/

https://www.quora.com/What-is-the-difference-between-exact-accurate-and-precise

https://english.stackexchange.com/q/96814

https://www.google.com/amp/s/www.englishforums.com/English/AccurateVsExactVsCorrect/bwprbl/amp.htm

https://www.google.com/amp/ask.metafilter.com/101373/Exact-and-precise/amp

https://www.waywordradio.org/discussion/topics/exact-vs-precise/

https://www.waywordradio.org/discussion/topics/exact-vs-precise/

https://www.google.com/amp/ask.metafilter.com/101373/Exact-and-precise/amp

https://www.e-education.psu.edu/styleforstudents/c3_p4.html

https://m.youtube.com/watch?v=hRAFPdDppzs

https://m.youtube.com/watch?v=_LL0uiOgh1E

https://m.youtube.com/watch?v=5-Dh2iFZC20

https://m.youtube.com/watch?v=KEeSQvMCPLg

https://m.youtube.com/watch?v=SLlTTB33vnY

Answer 1

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]

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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."

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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.