First of all, I want to clarify the difference:
Accuracy: Based on Wikipedia and what I've learned in class, accuracy is "the degree of closeness of measurements of a quantity to its actual (true) value."
Precision: Degree to which repeated measurements under unchanged conditions show the same results.
To be more specific, here are some figures:
(**Note:the vertical axis is % in total number of measurement, the vertical line indicates the actual value)
(1)poor accuracy good precision
(2)good accuracy good precision
(3)poor accuracy poor precision : (
(4)good accuracy poor precision
After the clarification, we can now finally focus on:
N[expression,{precision,accuracy}]
Let's see a few example and explain them
(1)precision>accuracy
-----------------------------------------------------------------------
----------------------------------------------------------------------- When using N[ ], you can think of it as you're "measuring" the actual value, that is 1/17, which is an exact number. So if you only asked Mathematica to "measure" the result with accuracy 4,but wanted it to display result as precision 13, it won't show that many digits cause the additional digits won't be correct(unless you want to mess up your calculation and end up with nonsense).
(2)precision<=accuracy
-----------------------------------------------------------------------
Now Mathematica is willing to display more digits since it has "measured" 1/17 with higher accuracy so now it's confident that the displayed result is correct.
p.s If you guys see any errors or stupid things I did in coding or explanation, feel free to correct me in the comments: )
