# I’m Done With Sig Figs

Posted August 10, 2012

on:This is not a new topic for me, it’s been a burr in my saddle for some time now. All of the introductory physics textbooks address significant figures in much the same way. The problem is – nobody in the “real world” uses sig figs. At the same time, introductory physics isn’t the time to introduce complex error analysis models.

I’m having this discussion with Andy Rundquist of Hamline University. I asked Andy how they handled this at the college level. He told me they don’t teach significant figures and pointed me to a very lengthy article discussing why significant figures are all wrong. The article suggests the use of Monte Carlo analysis its place. That may make sense on a lab, but not on classwork and homework problems. The uncertainty article did have a suggestion; use six significant figures for calculations and round the final answer to three sig figs. The article does a good job explaining the reasoning, and I’m fine with it. The three extra “guard digits” preserve the accuracy, and the rounding makes the answer more reasonable.

The next step is trying to explain uncertainty and significance of our data. I came up with an activity I think will work:

- I will project an archery target on the board.
- Students will move back about 20 feet and shoot a round of Nerf darts at the target. They will be far enough back that most of them will shoot a 6, or 7 and not a 9 or 10, at least at first. Each student will take a turn.
- We will plot the overall results. We should get something resembling a normal distribution curve, but I won’t tell them that.
- I will ask the kids to average the data and come up with a value of x.x +/- y.y and start a discussion on whether or not that represents the data.
- We will then put a ring or other object on an electronic scale and write the mass with the error in the same way.
- After some discussion, I will bring up slides of normal, rectangular, triangular, and maybe exponential distribution curves. I want them to discuss the fit of the models to the data.
- My goal is that they understand that error is probability.
- About a week later we will drop rulers and calculate individual reaction times. This would be a good time to bring back the distribution graphs and perhaps even input our data into a statistical analysis program to find the best fit.

I think this will work and go over well. I’d love some feedback. It’s a first pass, what did I miss?

### 7 Responses to "I’m Done With Sig Figs"

Very informative post indeed.. being enrolled in: http://www.wiziq.com/course/6911-advanced-placement-ap-physics

I was looking for such articles online to assist me and also your post helped me a lot.:)

Sig. figs were a quick and dirty way of dealing with measurement uncertainly when calculations had to be done manually. Nowadays “real scientists” don’t use signficant figures. They enter their data with explicit uncertainties and their statistical programs calculate the “error bars” of their resulting calculations.

Students need to know that measurements are not perfect, and that imperfect measurements can’t lead to perfect results. But requring them to know and use the sig. fig. rules seems to take up an awful lot of their time and mental energy. As far as I am concerned, it is just not worth it.

One of my former students came back to visit me. He is an engineer, working for NASA. They one thing he said I had better teach my students was significant figures!

1 | Charles Rodarte

August 13, 2012 at 5:56 pm

In Texas the new STAAR test is going to have some gridable questions. I am worried that my students are going to miss those if they do not use sig fig precisely as prescribed. So I think I’m stuck with the old way

Scott

August 13, 2012 at 6:20 pm

Interesting. On the AP Calculus exam, student are instructed to round everything to 3 decimal places. I just looked up the exam guidelines for AP Physics:

“Strict rules regarding significant digits are usually not applied to the scoring of numerical answers. However, in some cases answers containing too many digits may be penalized. In general, two to four significant digits are acceptable.”

I would like to believe that the writers of the test wouldn’t make the significant digits more stringent than the Calculus or Physics AP exams.