In everyday English, accurate and precise are generally used interchangeably. He gave a very accurate/precise description of the events. - The description was close to what happened. In maths, science, engineering, etc., they have slightly different meanings. 2 + 2 = 4 2 + 2 = 4.0 Both are accurate but the second one is more precise than the first. 2 + 2 = 4 2 + 2 = 3.9 The first is more accurate but less precise than the second and vice versa. So accuracy describes how close the thing is to the truth, whereas precision describes the degree to which the thing is expressed (like resolution on a TV or a camera). So often, greater precision leads to greater accuracy. Exact means correct in every detail - not approximated in any way. It is an ungradable adjective and is stronger than accurate, which is gradable. The answer was quite exact. - quite = completely The answer was quite accurate. - quite = somewhat, fairly, pretty, etc.

I think their meanings are pretty similar, but they are not interchangeable in all contexts. Exact is more related to Mathematics. You could say: the sum is exact. Accurate is more similar to "true" or "complete". You could say: "The report is accurate" if it has reliable sources and contains plenty of details. Precise is similar to "to the point". It means something similar to "reliable and without unnecessary information". I am not a native. Please check with one if you have the chance.

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.

"Precision", from its Latin roots, originates with the notion of the removal of all inessential elements: not too much, not too little. Just right. "Exact", from its Latin roots, originates with the notion of highly finished performance. "Accurate", from its Latin roots, originates with the notion of caring, or "done with care". All the words retain the emphasis presented by their roots. Here are some examples: Suppose you seek a Phillips screwdriver to fit a certain screw. If you find one that fits precisely, it means it fits the screw with neither too much nor too little extra wiggle. That would be a "precise" fit. You could also say the fit was "exact", but that word works better to describe a job well done. For example, you could say a singer sang a song "exactly" right, but "precise" and "accurate" would not seem like artistic choices. A student who gives correct answers to all the questions on an exam would be said to have given "accurate" answers, not "precise" or "exact" ones. He took the care to do it right.

Some additional points on accurate and precise: Precision can be thought of as repeatability expressed as a standard deviation or a similar statistical measure. In measurement science, a method can have a high level of precision, i.e. low variance between individual measurements, but exhibit poor accuracy/bias. Accuracy is how close something is to the true value or to the intended target. An individual measurement can be accurate (perhaps only by chance), but if subsequent measurements have a high degree of variance then the precision of the method is poor. Ideally, a measurement method has both acceptably high accuracy while exhibiting sufficient precision in order to provide utility. Reproducible deviation from the true value is often called bias. The visual of a dartboard is often used to demonstrate these concepts–i.e. precise but inaccurate dart throwing would see a tight grouping of darts far from the bullseye. An occasionally ‘accurate’ but imprecise dart-thrower could perhaps get one dart on the bullseye, but the ‘spread’ of the shots would be large and imprecise. Then, the dart-thrower who can maximize both accuracy and precision would be expected to win the game.