Precision versus accuracy

A few years ago someone explained the difference between precision and accuracy but I did not grasp it and am not sure I understand it now, except maybe with this example from recent experience with both digital and analog bathroom scales.
What is seems to me is precision is the refinement of the number being given.  For example, my new digital bathroom scale says I am 77.7 kg.  So it indicates a precision to the nearest tenth of a kilogram.  Whatsmore it will give this answer 3 times in a row from an off setting to the reading.  Now this could be just clever programming on the part of the scale manufacturer who makes the scale give the same reading as previously if the new reading is within say 1% of the previous measurement.  This would mean the scale would only need to remember one value when it is off.

Accuracy is an indication of how close the measurement is to reality.  If I actually weigh 50 kg and the scale says 77.7, it does not mean much that there is an indicated precision of about 0.1 kg when the real value is so different.  I would rather a scale give an accurate but less precise reading than a precisely inaccurate value.

This brings us to the confusing area of modern economic forecasting.  I recall a joke in the Economist many years ago:
Why do economists give their estimates of future events to the nearest tenth of a per cent?
Answer: To show they have a sense of humor.

Unfortunately, I suspect this is not the reason they give these kinds of responses.  I will let you list the numerous possibilities, most of which are not complimentary to the estimators, especially those employed by universities, governments, banks, and investment advisors.

It therefore pleased me recently to hear repeatedly that Ben Bernanke and other government financial officials were forecasting a weak recovery rather than giving precise numbers.  Having said that, there are frequently many reasons for government officials to lie about what they think and about what they know and that is not dependent upon the form of government.   While they try to appear upbeat about the future, this may in fact prevent actions being taken which would improve the situation.

So in general in the future I will try to be less precise and more accurate.  An easy approach to this is to give estimates in 3 classes: small, medium, or large. 
What will the US deficit be next year?  Large.
What are the chances the new US health insurance plan will be well executed?  Small.
What will future US petroleum imports be?  Large.
What are my chances of losing a little weight in the next year?  Medium.  I have to be a little optimistic or I won't even try.