Question

determine the amount of significant figures:
11 soccer players

Answer 1

@Xishem

Answer 2

would it be 11?

Answer 3

infinite. exact quantities of substances (or, in this case, people) have an infinite number of sig figs

Answer 4

thanks

Answer 5

an easy way to think of things like this, is to ask "can you measure the # of people any more exactly?" or "would you ever have 11.4 players?"

Answer 6

good point, thanks for the tip

Answer 7

There are two subtle aspects about this problem: first, the answer depends very much on whether you are talking about the number of players there are on a soccer team *by definition*, or whether you are saying you happen to observe 11 soccer players at a coffee shop.

If the former, then this is not a measurement at all, but what is sometimes called a "defined" or "exact" quantity, like the number of inches in a foot, or meters in a kilometer. Defined or exact quantities have no measurement uncertainty, because they're not measurements, and so it makes no sense to count their significant digits.

If the latter, then we do indeed have a measurement, and there may or may not be measurement uncertainty. It depends how we did the measurement. If we know we counted the players very carefully, and there is no chance at all we missed one or counted extra, then we might reasonably assign a measurement uncertainty of zero as JFraser points out.

But there are also circumstances in which our counting might have been hasty or otherwise prone to error, and then we might indeed assign a measurement uncertainty. For example, if I just glanced into the coffee shop and saw a bunch of soccer players, and you asked me how many, I might say "about 11," thinking it was somewhere between a handful and a dozen, and probably was just a complete team. We might quite reasonably assign that a measurement uncertainty of +/- 5 players, say, thinking if there were less than 6 I wouldn't have thought there were 11, nor if there were more than 16, but anywhere in between I might've been off a little. In that case, we might actually say my measurement of 11 players has only 1 significant digit.

It isn't very likely your instructor, particularly in an elementary class, is going to explain all this to you (although I think they should). But it's good to know. Usually, you're expected to say something like all integers have zero uncertainty.