What is the difference in meaning between exactly and precisely?

I want to say that there is exactly no difference, to be precise.

But… in my mind “precision” relates to measurement and judging things, and “exact” is a result of precise measurement or judgement.

Scientifically speaking, precision refers to the degree to which multiple measurements agree with one another. I’m not sure if there’s a scientific definition of “exact,” but I think they could be used interchangably outside of formal scientific writing.

I like @Mariah‘s definition of precision better. More precise than mine.

I would not use them interchangeably, but I think people might, in casual use, both as an intensifier and as an affirmation of another’s statement.

Playing by your rules and not peeking at any dictionary, large or small, hard or soft, I have to say that I think “exactly” signifies complete accord or congruence, whereas “precisely” indicates pinpoint accuracy. I would use them this way. But if I were editing someone else’s text, I doubt that I would ever call for replacing one with the other (unless in a scientific context such as @Mariah proposes). I might, however, call for deletion, not seeing any useful distinction between, say, “two inches” and “precisely two inches” if precision was not the issue.

But one can get either word as an answer in similar but non-scientific conversations.

For example, “is that what happened” and get back either “yes, exactly” or precisely.

“Exactly” to means I concur that they have achieved a satisfactory solution to their question or problem…
and
“Precisely” means that I concur that they have achieved a satisfactory solution to their question or problem as I see it!

In that example, @srmorgan, I think the intended meanings are identical, and the difference is in nothing other than a person’s habit of speech.

My son’s girlfriend has the habit of saying “Exactly!” to mean simply “yes, I agree, you’re right, that’s so.” After she’d been staying with us for a few weeks, I noticed that both my son and I were starting to say it. Then I met her mother and heard her say it half a dozen times in a short conversation. Now I am wondering what we used to say before for emphatic agreement. Maybe we just agreed without so much emphasis: “yes.”

Is it strictly a matter of gradation?

I am an accountant by training and used to getting an exact answer but not a precise answer.
In daily conversation I suppose the usages are interchangeable as noted here, but this has been buzzing around my head for, an inexact or imprecise, couple of days and I wanted to see what everyone thought.

I can go to a dictionary site. My guess is that Roget would like them as synonyms in general usage.

SRM

I don’t think my distinction was one of gradation. But contrary to a common perception, I am not a dictionary, so I would want to consult at least three references (OED, big Webster’s, and Am.Her. IV) before offering a definitive comment. Ok to peek now?

Roget might well group them together without implying that they are identical in meaning and connotation or interchangeable in use. The categories used in a thesaurus don’t necessarily group synonyms; other relationships are represented.

I don’t see the difference.

To me they’re about the same, but precise seems to be a little farther along on the scale toward minutiae.

Exactly accounts for a single attempt and achieving the result wanted.

Precision accounts for the getting the same result over and over again within the tolerable range.

In non technical language there is no difference between exactly and precisely other than perhaps precisely meaning “mostly correct” and exactly meaning “completely correct” .

How I see it:

SITUATION ONE:
Teacher: Gravity works on everything.
Student: Gravity will work on this apple.
Teacher: Exactly.

SITUATION TWO:
Teacher: Gravity will work on everything.
Student: So if I throw this apple in the air, it will fall down because gravity is acting on it?
Teacher: Precisely.

I think the difference is that one is commenting on having (essentially) the same idea. While the other is commenting on arriving at the same idea.

Apologies for the poor examples. But that’s the first thing that popped into my head.

@Nimis, I think you and I are making the same distinction:

“exactly” = complete accord or congruence
“precisely” = pinpoint accuracy

Do you think so too?