Question

A student counted 5 tables in the room. How many significant figures?
A. 1
B. 2
C. 3
D. 4
E. Infinite

Answer 1

thankyou!!!

Answer 2

E. Infinite. Significant digits are an indication of measurement uncertainty. One significant figure would mean that the number of tables in the room is 5 +/- 0.5, or somewhere between 4 and 6.

Does that sound realistic? Do you really think the student could have made any error at all in counting the number of tables? I don't think so. Which means the best thing to do is assign this measurement a measurement uncertainty of zero. If you think of number of significant digits, that means you have an infinite number of them.

Answer 3

^^ Exactly. The number of tables, 5, will be exactly the same as 5.0000000000 tables. I don't think a 5.1234 amount of tables exist. No matter how much zeroes you put after the decimal point, the answer remains.

Just remember that things that can be counted like people or objects have infinite significant numbers. :)

Answer 4

That isn't quite true, pnicole. It's not whether you can count them or not, it's whether or not you can reasonably assign measurement uncertainty, and if so, what it might.

For example, the Federal debt as of this very microsecond is an integer number of dollars I could read a statement from the Treasury that puts it at $15 trillion (1.5 x 10^13 dollars). That is in principle an integer, but of course that particular measurement only has 2 significant digits, at best. It would be very reasonable to assign a measurement uncertainty of +/- 0.5 trillion dollars to it.

Here's a more subtle example: suppose I could the cars going across the Golden Gate bridge. Case (1) I do it at 4 AM, and I get an answer of 12 cars in 30 minutes. What would be a reasonable measurement uncertainty there? Probably zero. It doesn't seem likely I missed a car or counted once twice. So this is an exact number, zero measurement uncertainty, infinite sig digs.

Case (2) I do it at 4 PM, and I get 6337 cars in 30 minutes -- counting by eye! Do you REALLY believe there's no chance I missed one or counted one twice? Ha! So here I might very reasonably assign a measurement uncertainty of +/- 100 cars, and report my result as 6.3 x 10^2 cars -- two sig digs.

Case (3) I do it at 4 PM, and I get 6337 cars in 30 minutes -- but I use an electronic counter hooked to a cable on the bridge. There's just about zero chance the electronic counter messed up. In this case, once again, I can reasonably assign a measurement uncertainty of zero, and this number has infinite sig digs.

The bottom line here is that you can't robotically assign significant digits based on whether a number is counted or not, an integer or not. You have to think about the meaning of significant digits -- which is that a measurement has measurement uncertainty. What is the uncertainty? This is the source of significant digits. Significants digits are not a property of a particular number -- but rather of a particularly measurement.