Friday, August 31, 2012

30 Second Science: Significant Figures

With some increased traffic to my blog, I'd like to do another "30 Second Science" - a quick post to explain some important or interesting aspect of science. Today we're gonna talk about significant figures.

Now, this is usually a topic that would be covered in a boring chemistry lecture - but it is very important. Significant figures are what determine to what point we can trust a measured value.

An example, grab your calculator. Ok, now: 

\frac{1}{{10}} = 0.1

This is not at all an unexpected result. So if we have one pie and ten people, each person will get one-tenth of the pie. But what if three people were to share four pies?

\frac{4}{3} = 1.33333333333333...
How are those pies to be divided? If we give each person one pie, there will be a whole pie left over. If we give each person 1.3 pies, there will be one-tenth left over. If every person gets 1.33, there will be one one-hundreth left over. If every person gets 1.333, we need a very accurate cutting device and we will still have one one-thousandths of a pie left over!

The answer is obvious, everyone gets about 1.3 pies, and someone gets a little more. This describes significant figures. When we make a scientific measurement, we need to know how many figures (numbers) are important.

A story to drive the point home
I heard this story from a member of my PhD committee. He once attended a lecture of a famous paleontologist. The speaker had brought with him a dinosaur bone. At one point he asked "How old do you think this bone is?"
A woman from the crowd responded "230 million and 5 years old"
"Excuse me," said the speaker, "You are correct, but why 'and 5 years'?"
"Well," the voice called back "I heard you speak five years ago and you said it was 230 million years old. That was five years ago."

I hope you can appreciate the humor in that remark. When the speaker had said it was 230 million years old, he had not meant.
230,000,000 years
but instead simply 230 million years - That is, only 3 significant figures.