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:
- a. Can you tell me the ...... time?
b. Yes, it's 4:26.
a. exact
b. precise
c. accurate
- I forgot the ........ age difference between them, but I think they're two or three years apart.
a. exact
b. precise
c. accurate
- a. Try to remember his ........ words. It's very inportant for us to make a decision.
a. exact
b. precise
c. accurate
- Can you remember her bitthday's ......... date?
a. exact
b. precise
c. accurate
- 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