In this lesson, we're going to learn about significant figures.
When students first learn about significant figures in chemistry or physics class you
always think it's like the most useless thing in the world and just a big waste of time.
Most people hate significant figures when they first learn it.
The problem is the one group of people who don't hate significant figures are teachers
which love them and teachers, also it seems, love to take points off tests when people
don't get their significant figures quite right so no matter what stage you are in learning
chemistry or physics even if you're in the middle the year it's a great help to refresh
significant figures and because there are plenty of points that can be earned on homework
assignments and quizzes and lab reports by brushing up on this very important topic.
The other thing is significant figures just aren't that hard if you really spend a little
bit of time practicing it.
One of the most difficult things about significant figures, I think, is that students just don't
really understand what they’re for, what the purpose of it is.
Well here, let me show you… here's an example.
Let's imagine that we want to do a pretty simple calculation.
We want to take 62 divided by 41.
We plug this into our calculator and we get really ugly answers.
The answer we get, the calculator is going to spit out, it’s going to be 1.512195122…
how’s that for an ugly answer?
Now here's the thing, you obviously don't want to put this whole thing down your sheets
so you're going to ask your teacher…how many numbers do we need to round to?
Well, that's the thing about significant figures.
If you understand significant figures you don’t need to ask your teacher that question
because the answer that question… how many numbers to be rounded to... is already answered
by the numbers you divide in the first place.
Let me show you what I mean.
I’ll give you a demonstration first and then I’ll explain the details.
62 has two significant figures…
a 6 and a 2… two significant figures.
41 has a 4 and a 1, also two significant figures.
That means I’m going to round the answer that I got to two numbers, simple as that.
So the 1 is going to stay and the 5's going to stay but remember I'm going to be rounding
so I'm going to have to look at the number next to the 5 to determine whether I keep
the 5 the same or if it's a big number I'm going to round up to 6.
In this case, it's a 1 so I don't roundup I keep it as 1.5 and that's my final answer.
The question of how many numbers I need to round it to is already answered by the number
of significant figures in the numbers that I divided together.
Now the question you may ask is how did I know that there were two significant figures
in the 62 and 41?
The answer is pretty simple.
Any number that isn't 0 is always a significant figure, we'll talk about 0 in the next lesson
‘cause it can get a little bit tricky.
Let's take a look at another example.
Let’s do 782 divided by 231…put that in the calculator again we get a really ugly
answer out 3.385…
I don't want to put that whole thing on my sheet either so I look at the numbers that
I divided together.
How many significance…
how many significant figures in 782?
Well none of them are 0 so three significant figures here, they're all significant…
231 none of them are 0, three significant figures here.
What does that mean?
It means I that I’m going to round my answer to three significant figures…
this is going to stay, this is going to stay, and this is going to stay.
As before I’m rounding so I look at the number to the right of this 8, it's a 5, which
means I'm going to have to round up… that 8 is going to become a 9 and my final answer
is going to be 3.39.
Again, it’s 3.39 because that 5 there makes me round the 8 up.
Let’s go one more example.
1219 divided by 3462, another pretty ugly number .352109.
How many numbers do I round it to?
I'm sure you've already gotten the hang of it.
Four significant figures here, four significant figures here… that means I round my answer
to, you guessed it, four significant figures.
This stays, this stays, this stays and this stays and I looked at the number just to the
right of the one it's a 0 so I certainly don't round it up.
My final answer is going to be .3521.
There you go, rounded four significant figures.
Now we can do this exact same thing with multiplication, all we have to do is round and then we add
a 0 if we need to.
Let me show you what I mean.
When I take 56 and multiply it by 28, the answer that I get is 1568 but as with division,
I look at the significant figures in the two numbers I multiplied together…
two here and two here… which means I'm going to round my final answer two numbers.
This one stays and this one stays and I look to the right of it to decide whether I round
up or down.
It's a 6 so I round up.
My final answer becomes 1600 because these two numbers stay and I just fill everything
else in with 0’s so I get 1600.
If I multiply these guys together, 4,833 times 1741, I get a really big number…
8,414,253.
Again, how can I round this using significant figures?
Four significant figures here and four significant figures here so you guessed it I round my
answer to four digits, I look here to figure out whether I round up or down, it’s a 2
so it stays the same…8414 and I fill the rest of the number in with 0’s.
I don’t need them… rounded to four digits.
Now if you're smart, you've already realized I'm doing something pretty simple.
All the numbers I’ve been multiplying together or dividing have the same numbers of significant
figures.
So maybe you're asking yourself…
okay this seems easy enough but what would I do if I had to multiply together or divide
two numbers that didn't have the same numbers of significant figures?
What if like for example, one had 5 and one had 2?
How would I round that?
Let's take a look.