accuracy = the state of being correct
precision = the degree to which correctness is expressed

For practical purposes, this means you shouldn't use these two words interchangeably. The above (admittedly complicated) diagram shows how engineers in some industries (e.g. aerospace and robotics) might look at the difference.

In this diagram, "knowledge" represents the range between where you should be and where you think you should be -- if your knowledge is perfect, then where you should be is a single point. Or a single answer. Likewise, "precision" represents the range between where you are and where you think you are. If you're perfectly precise, with the significant digits allowed by the problem, then you are where you think you are. If both knowledge and precision are perfect, you have no "uncertainty" about your answer; the "accuracy" is just the difference between where you are and where you should be -- the degree of correctness.

As if that isn't difficult enough to absorb: some answers are subject to real-time change. In some aerospace tasks they call this effect "jitter." It's hard to be accurate when the answers are moving around. :-)

In some types of engineering tasks, though, there's a "budget" on accuracy -- a level of jitter you can tolerate, a level of precision you must have, a level of knowledge you can settle for. The idea with the budget is to parcel out sources of uncertainty so that one source doesn't dominate the problem. Why be precise to five significant digits to the right of a decimal point when your knowledge is only as good as integers?

Here are some other (hopefully simpler) ways of looking at the difference:

• Accuracy is measured against a standard. Precision is based on the partial derivative of a measurement with respect to its contributing factors -- it's more a measurement of repeatability than an absolute.
• In process control, if a process yields the same results for the same inputs whenever those inputs are introduced, it's under control. But that doesn't mean the results are what you wanted. You're precise but not accurate.
• You can infer which of two accurate measurements is more precise; you can't infer which of two measurements of different precision is more accurate.
• You can shoot some number of arrows (call the number N) at a target. If all N are in the bullseye, then you're both accurate and precise. If they're within a small circle high and left of the bullseye, you're precise but not accurate. If you're within a large circle centered on the bullseye, you're accurate but not precise.

Does that help? :-)

Assignments

You can test accuracy from a robotics point of view simply. If you have two concentric cardboard tubes, joined at three points by rubber bands, you can look through the tube to locate a target, then "grab" the target by turning one tube relative to the other, tightening the rubber bands. What affects your accuracy?