Students will find that the closely related topics of significant digits, scientific notation, and error propagation will be useful in every experimental situation. In this session we will explore why these concepts are so important.
The students should understand the concepts of significant digits, scientific notation, and error propagation. They should understand why it is tempting to use too many digits. They should understand how errors are propagated through calculations and what the concept of error means in a statistical sense.
This lesson tends to be primarily a lecture format. Make every effort to get the students involved.
Here is a document that describes the general rules for significant digits, scientific notation and error propagation. It is probably enough to keep your class entertained for at least half the class period. The last part of the document is too complex to be of much use but it will help those very curious students.
Although we don't want to cover the details of a normal distribution in this session, we can provide an overview and indicate how a normal distribution is a very useful concept in physics. Begin by putting a strip of masking tape on the floor at one end of the room. Have each of the students toss a handful of stones in an attempt to get closest to the tape. (One at a time is fine but 10 at a time will go a lot faster.) Record the distance from the tape. Don't use a computer. It is important for the students to "feel" this calculation. (It would be good to have a reward for the student who has the closest average toss.) Calculate the mean position of the stones from the tape. Calculate the variance (sum of the squares of the deviation from the mean) and standard deviation, σ as the square root of the variance.
Think this through so that you can distribute the calculation among all the students and get it done quickly.
Finally plot the distribution of the stones. Use histogram bins that are one standard deviation wide and count all the stones that lie within that bin. There will be a bin on both sides of the taped line. Plot that number of stones in each bin as a function of σ. Note: The instructor may want to use smaller bins to get a better approximation to a normal curve but don't get too small because there will be very few counts in each bin.
The relationship between the calculated standard deviation and the standard deviation of a normal curve is profound but it will have to remain somewhat mystical for this session. Measurement errors often have a standard distribution as indicated by the curve above.
Evaluation questions on significant digits, scientific notation, error propagation, and the normal distribution are a dime a dozen so pick a few for the students.