significant figures

I have had a request to write a post on significant figures!! So, here we go….

There is one simple rule for you to follow. Look at the information you are putting in to your calculation, and identify the value that has the fewest significant figures – this is the number of significant figures you will put in your answer!  It is that simple.

An example:

Lets look at the question in your 109 workbook (workshop 2) on the mass of the whale plus all the barnacles, micro-crustaceans and bacteria on that whale….

Lets just think about the mass of all of those micro crustaceans. You are told that a micro crustacean weighs 0.5 mg, and that there are 150 of them on one barnacle, and there are 34000 barnacles on the whale. So what is the total mass of the micro crustaceans on the whale?

This is a simple enough question, you just multiply the mass of one micro crustacean with how many micro crustaceans you have on one barnacle, by how many barnacles you have on one whale:

0.5 mg x 150 x 34000 = 2550000 mg (which is the same as 2550 g)

So, a whale has 2550 g of micro crustaceans on it….

But how many significant figures should our answer have? The answer is one! Our answer should be 3000 g.

Why is this? Well look at the values you put in, you know the mass of one micro crustacean to one significant figure (0.5 mg), and you know the number of micro crustaceans and barnacles to two significant figures (150 and 34000). So your least precise value in your calculation was the mass, and therefore your answer cannot be more precise than one significant figure.

Lets have another example:

Lets say you have a question that asks you calculate how fast a golden eagle flies.  You might be told that the eagle flies 255.4 km in 2.0 hours, and so you can use this to calculate the speed.

So, the speed of the eagle in km/hour will be 255.4km/2.0hours = 127.7 km/hour. 

Great, but now you have to write this answer to the correct number of significant figures.  Look at the information you put in to the calculation. 255.4 km has four significant figures and 2.0 has two significant figures. Therefore, you want to write your answer to two significant figures, so your answer is 130 km/hour.

Why is this?

Again, this is all about precision. You know the distance the bird flies to four significant figures (255.4 km), but you only know the time it takes to fly this distance to two significant figures (2.0 hours). 

So, the time taken could be 2.01 hours, or 2.04 hours, or 1.99 hours, or 1.95 hours….I could go on. The point is, the time is only given to two significant figures, but this could well have been rounded from other values, or the measuring device was not able to measure the time to a greater level of precision.

The fact is, beyond 2.0 hours, you don’t know the time more precisely than to two significant figures, even though there could be a bit more time or a bit less time taken for the bird to fly 255.4 km.

So, when you write your answer, you have to stick to the amount of significant figures of your least precise measurement, as beyond that number of significant figures you cannot be sure that your answer is exactly correct. So in this case, use two significant figures :)

I hope that helps you all out!

Oh, and make sure you know how to tell how many significant figures a value has!  This might seem simple, but some situations could catch you out, here are some examples:

201  this has 3 significant figures

20.1  this has 3 significant figures

2   this has 1 significant figure

2.00 this has 3 significant figures

0.00004   this has 1 significant figure

0.004055  this has 4 significant figures

0.0400  this has 3 significant figures

Hurrah for significant figures!