Emily had trouble answering one of her homework questions for math class: “What is more accurate: a measurement given in centimeters or a measurement given in millimeters?”

The author of this question made the classic mistake of confusing precision and accuracy. *Precision* is about being well defined while accuracy is about correctness. The unit in which a measurement is given has nothing to do with its accuracy (unless the unit is incorrect of course).

Take, for example, the question “What is the value of pi?” An answer of “2.78495718397583711985” would be very precise but not accurate. An answer of “3.14” would be accurate but not necessarily precise. The amount of precision needed depends upon who’s asking the question. If your math teacher asks you “What is the value of pi?” then the answer “3.14” would be accurate and precise enough for the situation. However, if a NASA engineer is calculating orbits for the space shuttle and asks you for the value of pi, “3.14” is probably not going to cut it. Space shuttle orbits require significantly more precision, say, 3.14159265358979323846264338327950288419716939937510

What? NASA engineers aren’t regularly asking you for the value of pi? Well, it must just be you, buddy, because I’ve got NASA engineers calling me night and day wanting to know the value of pi. It’s a good thing I know all about precision and accuracy.

So, in answer to the question “What is more accurate: a measurement given in centimeters or a measurement given in millimeters?”, I had Emily write the following:

“Neither. A measurement given in millimeters may be more precise but not necessarily more accurate.”

I then wrote a little explanatory paragraph below her answer:

“Emily’s Dad thinks this is a poor question because it confuses the concepts of precision and accuracy”.

Who knows, maybe Emily’s teacher is a former NASA engineer and will appreciate an answer like that? Now, if we can just get Emily through fractions we’ll be making good progress…