some notes below
Precision means the variability between estimates Accuracy means the amount of deviation between the estimate and the "true value"
The condition number is the ratio of the output error to the input error. if the condition number is about 10k, then one loses about k digits of accuracy.
The main sources of inaccuracy (= error) is truncation error and round-off error.
From the above dart diagram, then we can say this: a value is accurate if it is near the bull-eye. But if is away from the bull-eye, but it is always away from the bull-eye and in the same place, then it is precise. So something can be precise but not accurate. So precise has to do with repeated values. i.e. one can’t say a value is precise, but must talk about an experiment being precise, it is produced same result each time (or very close results each time).
So, it is best of course to be both accurate and precise. So what does it mean to be accurate but not precise? using the above dart diagram, it means values generated from the experiment are always close to the pull eye, but not in the same locations.
From http://forums.wolfram.com/mathgroup/archive/2010/Jan/msg00917.html
The definition of precision in Mathematica is this. Suppose x is a number known up to an error of epsilon, that is it can be viewed as lying in the interval (x-epsilon/2,x+epsilon/2). Then its precision is -Log[10,epsilon/x]. Its accuracy is -Log[10,epsilon]. The two are related by the equation: Precision[x] - Accuracy[x] == RealExponent[x] The interpretation in terms of digits is only approximate. Both accuracy and precision can be negative - this depends on the scale of the number i.e. RealExponent. A number will have negative accuracy if its absolute error is large. It is easy to produce such numbers by cancellation With[{x = N[10^100, 50] - N[10^100, 50]}, Accuracy[x]] -50.301 On the other hand, since $MinPrecision 0 You won't normally in Mathematica see numbers with negative Precision. Precision is the main concept, Accuracy is only used because Precision is singular at 0 (remember - its relative error). It's all perfectly documented so this tired scape goat is not available this time.