When you tutor chemistry or physics, significant figures are a constant theme. Some people call them significant digits. We’ll start our explanation today.
Bill: How heavy is that boat?
Joe: Maybe 30 tons, give or take a couple.
Bill: Then it’s 30 tons, 40 pounds. I see a sandbag on deck.
The conversation above illustrates the concept of significant figures. If a boat’s mass is 30 tons, give or take two tons, that puts its mass anywhere from 28 to 32 tons. In that context, a 40 pound sandbag is not significant: we can’t know the mass to the exact number of pounds, when we don’t even know the exact number of tons.
Here’s another illustration: let’s say you know Susan’s house is 3km from Sherry’s. Sherry lives in a town that’s around 800km away. However, “around 800km” means between 750km and 850km. Can you say that if Sherry lives “around 800km” away, Susan must live 803km away? Once again, the 3km difference is not significant, since there is a 100km range in the actual distance to the town.
Physics and chemistry use significant figures (sig figs)- aka, significant digits (sig digs) -to reflect the reliability of any measurement – i.e., how precisely that measurement is actually known. The system is relatively straightforward in most cases, but takes some getting used to.
Now that we know the purpose of significant figures, we’ll discuss how to treat them in the next few posts.