I want to give you some practice with scientific notation so in this video I'm going to do
12 example problems, step by step, so by the end the steps should be really easy.
Here's our first example, 483 we want to put it into scientific notation.
So where's the decimal point?
Well it's not written in this number but we know that it's right here so I'm going to
put it in.
Now, to put this in scientific notation we need to move this decimal place so there is
only one digit, one digit that isn't 0, to its left okay?
So that means I'm going to move the decimal place over two spots so that it�s right
here and I have just one digit and that's the four that is to the left of it and then
everything else is on the other side.
So I could rewrite this number as 4.83 because I move the decimal place to here.
That's half of it.
Now the other half of scientific notation is that we have 10 with an exponent on it.
So what's the exponent on 10 going to be in this example?
Well I like to think that we start out when the decimal place is here, we start out with
the exponent being 0, decimal place is here and we are starting out 10 to the 0 and then
when I move the decimal place to the left, what I have right here, the exponent on 10
goes up.
Okay?
So I started at 10 to the 0 here, move it one spot and now it's 10 to the first, move
it another spot now it's 10 to the second.
So the exponent part of my number is going to be 10 to the second because I'm moved this
decimal place two spots to the left and the exponent went up.
So 4.83 times 10 to the second.
This number over here is already written in scientific notation so I want to get it out
of scientific notation.
I'm starting at 10 to the fifth here and to take a number out of scientific notation,
I want to move the decimal place so that this number on 10, the exponent, goes back down
to 0.
Okay?
So it's a 5 right now and I want the exponent to go down.
So take a look at these rules up here.
I want to move the decimal place to the right so that the exponent will go down.
So, I have 3.001 and right now I'm at 10 to the fifth so moving it right one spot I'm
at 10 to the fourth.
Okay?
Move it right another spot, 10 the third, 10 to the second, 10 to the first, 10 to the
0 and here's my new decimal place.
Now you'll see that I moved the decimal point beyond where there were numbers, I ran out
of some of these digits and I introduced two new spots.
All you got to do is fill those in with zeros if that happens so when I rewrite my number
so it's a little bit neater I end up with 300,100 and again all I did was move the decimal
place to the right so that the exponent went down from 5 down to 0.
Okay?
We want to write this in scientific notation so I want to move the decimal place so there
is one number that isn't a 0 to the left of it.
So these are all 0's so I'm going to move past all these and I'm going to put it right
here so I have a 2, that's not a 0 and it's to the left of where the decimal place is
going to be.
We'll be moving it to the right which means the exponent on the 10 is going down.
As we said before, if a number isn't already written in scientific notation, it starts
at 10 to the 0.
So when the decimal place is right here we at 10 to the 0.
Now we move it to the right and we're going to start going lower than 1 so we can get
into the negatives.
So we start at 0 then we go to 10 to the negative first, 10 to the negative second, 10 to the
negative third, 10 to the negative fourth, and the negative fifth, 10 to the negative
sixth, 10 to the negative seventh, and our new decimal spot location is right here so
when I rewrite the number.
I don't worry about any of these 0's here because they all come before this non-zero
digit and then I write 2.3 times 10 to the negative seventh.
This number here I want to take it out of scientific notation so I get 10 to the negative
fourth here I'm going to be moving the decimal place so that this negative fourth comes back
up to 0.
Now notice this is a negative number here, some people get confused by this but the negative
number in front of 7.6 has nothing to do with the negative number in the exponent so don't
be confused by this.
They are totally separate.
So what I usually do is I just leave this negative sign out until the very end and I
put it back in.
Anyway, I'm starting with 7.6.
We want this 10 to the negative fourth to come back up to 0.
We want to move up, exponent moving up, so we'll move the decimal place to the left.
Okay?
Starting at 10 to the negative fourth, negative third, negative second, negative first, 0.
I introduced a few new spots and I'll fill those in with 0's.
The final answer will be 0.00076.
Don't forget that it's a negative number so we'll add that negative sign there and this
is what our final answer taken out of scientific notation looks like.
Now here are a couple example problems that are a little bit trickier, sometimes people
get tripped up by some of what's in here so I'll go through here step-by-step.
We'll be taking this number, putting it in to scientific notation.
There isn't a decimal place written in right now but we know that it should be here so
I'll draw it there now.
I want to move the decimal place so, all the way over here, so that there is this 8 to
the left of it.
Everything else is on the other side and since I'll be moving it to the left, the exponent
on 10 will be going up.
We started 10 to the 0 because it's not yet in scientific notation, we're moving up, 10
to the first, 10 to the second, 10 to the third, 10 the fourth, 10 the fifth, 10 to
the sixth, 10 to the seventh.
So that's that part of it and now I'm going to do 8 and what else?
Nothing else, okay?
It's just 8.
This can be confusing because we're so used to scientific notation always been like 8.113
or 8.865 but we also get rid of these zeros, okay?
So if there's nothing except for zeros to the right of the decimal place, just leave
it out.
This is an 8 point anything, we don't even write the decimal place in here, okay?
It's just 8 times 10 the seventh.
We'll put this, we'll get this out of scientific notation and start with 4.29.
I'm at 10 to the negative first so I want to go up to 10 to the 0.
So I want the exponent to go up, this means that I'll be moving the decimal place to the
left.
So 10 to the negative first right here, move it one spot to the left and now it's 10 to
the 0.
So 0.429 so you have to move the decimal place but sometimes you don't have to move it very
far.
-9 times 10 to the fifth, this is kind of like this one here because we just have one
number, no decimal place, nothing after the decimal place but you know where the decimal
place should be.
So, we'll write it in here like 9 point because that's where the decimal would be, it's a
negative number, we'll leave that negative out until the very end.
It doesn't have any bearing on what we're going to be doing with the decimal.
So to be getting it out of scientific notation, we'll be taking the 10 to the fifth and bumping
that exponent back down to zero.
To get the exponent down, we'll be moving the decimal place to the right here, okay?
Starts at 10 to the fifth, 10 to the fourth, 10 to the third, 10 to the second, 10 to the
first, 10 to the 0.
I introduced a lot of new spaces here, fill those in with zeros, and 900,000 is what I
get.
Don't forget to make it negative and that's the final answer.
Here, we're going to put it in to scientific notation, again it's negative, you should
leave that until the very end.
I'll have to put in the decimal because it wasn't already written here.
I'll be moving it all the way over here, moving to the left so the exponent on10 is going
to be going up.
Starting at 10 to the 0, 10 to the first, 10 to the second, 10 to the third, 10 to the
fourth, 10 to the fifth, 10 to sixth.
And the decimal place ends up right here.
Sometimes that confuses people because they're used to having, they're used to getting rid
of the zeros on one side of the decimal places like what do I do here because they're zeroes
here but then there's this 2, right?
Well we keep any zeros that are between numbers that are not 0's, okay?
So there's a 1 here and there's a two here so we keep all the 0's that are in between
them but then these 0's here that are all the way on the right, we will get rid of these.
Our final answer's going to look like 1.002 and that's negative so we keep these because
they're between the non-zero numbers but then we get rid of everything there on the right
so that's what that looks like.
I got four more here, if you really have gotten the hang of this, no need to keep watching
but little practice can't hurt if you're still feeling a little uncertain.
Start here, put in scientific notation.
I'm going to be moving the decimal place in this direction to the right so the exponent
goes down.
Starting at 10 to the 0, 10 to the negative first, 10 to the negative second, 10 to the
negative third, 10 to the negative fourth, 10 to the negative fifth, 10 to the negative
sixth, 10 to the negative seventh.
There's a 0 here but it's sandwiched between these two nonzero digits so don't worry about
it.
I totally forgot what the exponent was -1, -2, -3, -4, -5, -6, -7.
Times 10 to the -7, thanks for hanging in there with me.
3.08 times 10 to the -7.
Take this out of scientific notation 9.53, I'm starting at negative 6.
I got to go up to 0 so I'm going to be moving the decimal place left so the exponent goes
up.
Negative 6, negative 5, negative 4, negative 3, negative 2, negative 1, 0.
Fill in each one of these new spaces with a 0 and I get 0.00000953.
Okay, two more!
Put this in to scientific notation, decimal place is here, moving right, exponent goes
down, start at 10 to the 0, 10 to the negative 1, 10 to the negative 2, 10 to the negative
3, 10 to the negative 4, 10 to the negative 5.
5.713, we don't keep any of the zeroes here that are on the left hand side, and this is
our final answer.
Okay and finally we are going to take this out of scientific notation.
Starting at 10 to the second, we want to get that to 10 to the 0, we want the exponent
to go down so I'm going to move the decimal place to the right.
So 10 to the second, 10 to the first, and 10 to the 0: 324.8.
Sometimes questions like this confuse people because they're used to moving the decimal
place beyond where there are numbers, right?
Where you have to like add in 0's or get rid of 0's but sometimes all you have to do is
just move the decimal place in between digits like here.
Just because you're not adding or getting rid of 0's doesn't mean you're doing anything
wrong.
Sometimes all you have to do is move the decimal place a couple spots like this, you don't
introduced or get rid of any zeros, it's fine.
Okay, so that's how you do the scientific notation problems, just a few things you got
to keep in mind.
If you move the decimal place to the left the exponent on 10 goes up, if you move the
decimal place to right the exponent on 10 goes down.
If your number is not yet in scientific notation you start at 10 to the 0 and if your number
is already in scientific notation like these, you want to move the decimal place to get
exponent on 10 either up to 0 or down to 0.
So that's all you got to do.
Now, if you have time please, please, please watch the video called understanding scientific
notation.
It's good to be able to move the decimal place back and forth and change the exponent on
10.
That's great, it's an important skill.
But it's just important to understand the math behind what's actually going on here
so you can do more than just move the decimal place but you can look at a number like this
and really understand what's going on.
So please, please, please watch that if you have the time but if you don't, if this is
the only time you have, you'll be great.
This is a really solid foundation for how to write numbers in scientific notation and
how to get numbers out of scientific notation.