# Scientific Notation

Alright, let’s take a look at lesson 4.
Alright, let’s revisit the challenge question for a minute.
It says, the NASA Data Archive at the Goddard
Space Flight Center contains 24 terabytes
of data from previous science missions. How many CD-ROMS
does this equal, if the capacity of a CD-ROM is approximately
6 times 10 to the- 10 to the eighth bytes,
and 1 terabyte is 10 to the 15 bytes? Ok, now, listen,
that’s- tho- that problem has huge numbers in it. Do you see
6 times 10 to the eighth? That’s actually a special
form of a number, ok. And we’re going to talk more
this challenge question when we know- when we understand
a little bit more. Ok, so let’s take a look at this
table, below, and let’s see if we can fill it out. Ok. So
the first thing is, 6.98, it says 6.98 and it’s multiplied by 10 to
the second. So we’re multiplying 6.98 times 10 to the second.
10 to the second really means t-
10 squared, which is 100. So you’re really
taking 6.98 and multiplying it by 100. We know what happens.
We know we have to move the decimal point, to the
right 2 places. So that’s going to be 698. Ok. Next we have 6.98 times 10 to the first.
That’s just 10. If we multiply by 10, it moves
1 place to the right. 69.8. And now we have 6.98 times 10 to the 0. Oh, 10 to the 0. Remembering
from one of the other lessons we’ve done. 10 to the 0, anything to the
0 power is 1, so this is really 6.98 times 10 to the 0, or 6.98
times 1, which is 6.98. Now, we have 6.98 times 10 to the negative 1. Now listen,
the pattern, look what’s going on. Here, we- here are the
decimal places, uh, at the end. Here it’s before the 8, here it’s before the 9.
So it keeps moving, so I- I almost would guarantee
if you follow our pattern, this would be .698. But why is that so?
We have to figure out what this really means. So let’s go, and take a look.
9 8 times 10 to the negative 1. 10 to the negative 1, remember, negative 1
means the reciprocal of 10 to the first. We just learned that about
negative reciprocals. So this is really 1 tenth. So
really what you’re doing, 10 to the negative 1
is really 1 tenth, so really what you’re doing,
is you’re dividing by 10. So you’re taking
6.98 and dividing by 10. We know when we divide
by a power of 10, the decimal moves to the left.
And it’s 1 place because there’s 1 0. So
that is .698, because actually what you’re
doing with these negative exponents is
you’re really dividing this number. Ok. Let’s
look at the last example. The last example is
6.98 times 10 to the negative 2. That means 10 to the
negative 2 is really 1 over 10 squared, or 1 over 100. So you’re really dividing
this number by 100, which means I’m moving the decimal 2 places,
2 places to the left. Which is .0698. So, what pattern do I see?
Well I- these are called powers of 10. Powers of 10 mean
that my base is 10, and I have some kind of exponent. Ok. So that’s a power
of 10. When I multiply by a power of 10 notice this. When I have a natural
number, 1 2 3, ok, I move the decimal p- point
to the right, those many places. I- this
tells me don’t move my decimal at all. This
tells me move my decimal to the left, if I have
a negative exponent. So that’s what I know, these are called
powers of 10. This whole entire number, 6.98- let- I’m going to erase
this for a second. 6.98 times 10 to the second, this whole expression
here, this whole expression, is called- is written in-
scientific, scientific notation. Scientific notation is used to write very big, or very
very small numbers, ok. So this is in scientific notation. This number, after
we multiply it out, is called standard, standard form. So if we take a look
at the next slide in your workbook, it kind of defines
for you scientific notation. Scientific
notation in number- this number, has to be between
1 and 10 including the 1. That’s why it
says this, right, watch. 1 is less than or equal to
the absolute value of A- we’re going to talk about
that- which is less than 10. And then it says,
and must be an integer. Oh- I, I left out the most important part.
All that- must be- can you see that? That was bad. An integer. It
gives me this little form, right above it. It says
A times 10 to the N. So A must be an integer, ok. And the
absolute value of A must be between 1 and 10. So- including the 1. So this is
fine, 6.98, because it’s between 1 and 10. This is also fine. Negative
4 times 10 to the negative 1. N is an integer, negative 1’s an
integer, and the absolute value of A, the absolute value of A, which is
4 here, must be between 1 and 10, which it is. So, we can have a
negative number here, as- ok, as well. But we can’t have something
that looks like this, .098 times 10 to the third. That is not
considered scientific notation. Why not? Because this A here, this is called
A, A is not between 1 and 10. So, we- we need to know when our numbers
are in scientific notation, and when they’re not in
scientific notation. So let’s take a look at some problems.
Alright, we just talked a little bit about scientific
notation, and remember we said that scientific notation was in
the form A times 10 to the N, which means you have 2 factors, ok,
because these are attached by multiplication, and
this X is a times, ok, a multiplication sign, ok. If
that’s a little confusing you can put a dot in there, but you’re
not going to see the dot in most textbooks or- or most, most worksheets.
You’re going to see the X, ok. The A remember has to be between
1 and 10, the absolute value of A has to be between 1 and 10.
And this must be a power of 10, which
means the base must be 10, to some integer exponent.
That’s how you define scientific notation. So I’m
going to do the first one with you, ok, I’m going to look at
all the parts, all the factors. Remember we have to be attached
by multiplication, and we are, ok. Now I’m going to look here.
This number has to be between 1 and 10. And it’s not.
Ok, that number is less than 1, therefore this is not scientific notation.
This factor is fine, because it’s a
power of 10, but here we lose it. So this is not in
scientific notation. Not scientific notation. So that’s all I’m asking
you to do, I’m not asking you to multiply, I’m not asking you
to do anything else. Just inform us if these are in scientific notation.
So I’m going to ask you to do 2 through
6, stop the video, do 2 through 6 in your workbook, and
then, and then we’ll go over them. Alright, how do you think you did?
Let’s take a look. Alright. 62. Well there’s already a problem, isn’t
there. 62 is not between 1 and 10. So this is not in
scientific notation. Ok. And 4.21 times 10 to the negative 4. Well let’s look at
the 4.21, that number is between 1 and 10, so that’s fine. That’s a
base of 10, to an integer exponent, so this is all good.
Attached by multiplication. So yes, this is in scientific notation.
Alright. Let’s take a look at number 4. 1 times 10
to the negative 8. 1, 1 is fine, because
remember it’s got to be between 1 and 10 including the 1.
So that’s fine. It’s attached
by multiplication, base is 10, to an integer exponent.
So this is another yes. So this is
is ok, the first factor is ok because that’s
between 1 and 10. We- attached by multiplication,
so that’s good. But here’s the problem. We cannot have a
base of 4, it’s got to be a base of 10. So this is not in
scientific notation. Ok so that’s no good. Alright, last one.
Negative 6.8. We have to make sure the absolute value of this
number is between 1 and 10, and it is. Because the absolute value of
negative 6.8 is 6.8. So that’s ok. That’s fine, that factor’s fine.
It’s attached by multiplication, great, and
that is a power of 10, to an integer exponent, so yes, all of
these are in scientific notation. Ok? In the next slide, we’re
going to ask you to express some examples in standard form.
All that means to do, is to take it from
scientific notation, and multiply it out.
Remember how to do that. I’m going to show you right here.
If we take this one, and put it in standard form, it
means that we look at the exponent, and if it’s
negative we move the decimal to the left, that many places.
Of course I picked a big one, alright.
But here’s your decimal, 1 point. We
want to move it 8 places to the left. I’m going
to move this over so I have enough room to move
it 8 places to the left. Ok. I’m going to have to add 7 0,
there’s 1 place, but now I have to start- adding 0s. So it’s 7 0s.
1, 2, 3, 4, 5, 6, 7, and there’s your 1.
Right, because 1, 2, 3, 4, 5- I missed one, sorry.
1, 2, 3, 4, 5, 6, 7, 8. When- when you
get older, you start seeing lots and lots
of 0s when you look at 0s. Ok. Yeah, look forward to that.
Anyway, so, that’s my number in standard form, that’s my number
in scientific notation. So, just do the
next 3, put them in standard form, and
we’ll revisit that. Alright, here we go.
Let’s see how you did. Positive exponent, we’re
going to move the decimal 5 places to the right.
So we’re going to take 2.451, and we’re going to move it once,
twice, 3 times, we’re going to have to add 2 0s to make 5 times.
So 245100. Take the decimal out of the number,
because the decimal is now here. Don’t keep the decimal there,
because then you haven’t changed the number. Ok. So this is your
final answer in standard form. Ok. This guy- we have a negative
exponent, so we’re going to move the decimal to the
left, that many places, which is 3. So we have 7.31.
Here’s 1, 2, 3. So .00731, that
is your number in standard form. Pretty easy, right?
And last one, that just means- don’t, don’t move at all, no
spaces, no spaces. Because remember why, we’re
multiplying by 1. So your answer there is negative 5.5. So now
we know the difference between standard form and scientific notation.
We know what it means for a number to be in scientific notation.
Now we’re going to figure out, how do we take
a number and put it into scientific notation. So
that’s what we’re going to do next. Alright. This
number is 640, it’s really considered standard form.
I’m going to put this number in scientific notation.
So- you can follow the steps that are on- in
I’m going to put my- my decimal point,
remember it’s here right now, this is where it is right now.
I’m going to put my decimal to the f- to the
right, of the furthest non-zero digit. So the first number
that’s, reading from left to right, first number that’s not
0, that’s, that’s where my decimal is going to
go to the right of. So if I write this number, 6, ok. That’s
the first digit that’s not 0, I want my decimal to be right here. Maybe
I’ll make an X right there. Ok. So that’s where I want it.
Now I have to say to myself- listen to this,
this is the hard part, this is the part I don’t do ver-
I didn’t do very well a long time ago, because I’m a little dyslexic.
So this made me crazy. But here’s what I
have to do- say to myself. I have to say to myself, Self-
yep, I did say that- Self, how many times do I have to move my d-
you remember, because remember now, it’s times 10 to some power.
Here’s how you get the power. How many
times do I have to move this where I want it, back to where
it was, back to the original? So here’s where it wa- whoops. Here’s
where it was. It was right there. I have to move it 2 places, and I have
to- look, I- to- to get it back where it was, I have to move it 2 places to
the right. That makes it a positive 2. The biggest error people
make, is they say, oh, I want it here, well I moved
it 2 places to the left. Eh- eh. That’s wrong.
Because I have to get it back to the original.
So my number now is 6.40 times 10 to the second.
Because I moved it, had to move it to the right, to get it
to the original number. So this number is my
answer in scientific notation, and I can check that. I can
check that by multiplying. If I was to multiply this, I’d have to move the
decimal 2 places to the right. If I move the decimal 2 places to
the right, I will get back to this number.
That’s how you check it. Now listen. As a dyslexic,
that made me absolutely crazy. I always wanted to put a negative when
it was positive and a positive when it was negative. So I’m going to give
you a little- well, I’m not going to give you the hint yet. Wait
until we do this one, maybe you can give me the hint. Ok, so
that’s the answer to that problem. That’s that number in scientific notation.
So these mean the same exact thing, only one’s written in
scientific notation, and one’s written in standard form.
Ok? Alright. Take a look at this one. So the first
thing we do, is we put the decimal to the right of the first non-zero
dig- digit, I was looking for my blue pen, if you were
looking at me, looking at me weird. Ok, to the right of the first
non-zero digit. Well the first non-zero digit- that’s 0, that’s
0, that’s not 0, non-zero- that’s where I want it,
I want it right there. Ok. And again, I’m going
to make it almost look like an X kind of guy.
Ok. So I’m going to do 9.8- I don’t need
these 0s in the front, when I put 0s in the front
they’re meaningless. So 9.8, and remember
it’s times 10 and I’ve got to figure
out what power. Now here’s the deal. Remember
I have to take it back to the original. Well
this is where I want it, because I need it
to be between 1 and 10 and now it’s between 1 and 10, but I have
to get it back to the original. 1, 2, 3. And notice I’m going to the
left, so that is a negative 3. So it’s 9.8 times 10
to the negative 3. That’s that number in scientific notation.
Don’t believe me? Check. If I multiply this, I have to
take it 3 places to the left. So 3 places to the left
would be 1, add 2 0s. And that’s my original number.
I’m just writing my original number in another way.
Ok. So. You think you know
the little trick I was going to tell you?
Here’s the little trick. And this is in your
notes, I’m not going to write it down, ok. If
the given number, this is the given number, is
bigger than 1, you’re going to have a positive exponent.
If the given number is negative- is
uh, less than 1, this is less than 1. You’re going
to have a negative exponent. I like that, because
then I don’t care which way I’m moving it. I just
put it where I want it and count. I don’t have to worry,
is it negative, is it positive, that’s too hard for me. So,
this makes that a lot easier. The given number’s pos- uh, bigger than 1.
Positive exponent. Big- uh, given number is less than
1, negative exponent. Makes it a lot easier to deal with.
So that’s how you do it. On your next slide there are 6
problems, ok. I want you to try 1, 2, or 3, believe it or not. 1, 2,
and 3, believe it or not. And then I’m going to come back and
go over those, and do 4, 5, and 6. In number 3 it’s
negative, don’t worry about the negative.
When you put the number in scientific notation forget
about the negative, and then just bring down the negative.
So try those. Alright, let’s see how you did. Let’s go to number 1. Ok. That number’s
bigger than 1, so I have to tell you, I already know that I’m going
to have a positive exponent. And you know what, I’m going
to make that box just a little bigger, just in case you can’t see that.
Well I do have a new handy-dandy marker. That’s a positive,
that’s to remind me it’s positive. Ok, now here’s
what I want to do. I want to put this decimal, remember,
to the right of the first non-zero digit, and that’s right there,
3.68. Remember why I want to do that. That puts it between 1 and 10. Ok. So it’s
3.68, and now I have to say to myself, how do I get it back? Well I get
it back to the original by moving 1 spot. So it’s positive 1.
So it’s 3.68 times 10 to the first. Ok, and I knew it was
positive because that number’s bigger than 1. But I can tell it’s
positive because they have to move 1 to the right to get
back to the original. It’s ok, it’s just a little bomb.
No it’s, it’s my marker top. Ok. Here we go. Positive
or negative exponent. Yes, it is a positive- sorry,
negative exponent, because it’s less than 1.
This number, this given number is less than 1.
So it’s a negative exponent. Ok. So now, I want it to the right
of the first non-zero digit, m- my decimal. So, 0’s a 0, 0’s a 0,
here’s 4. 4 is not a 0. So that’s where I want it. If I want to write 4.0 I
can, I don’t have to. Ok. But I want it here. I want it right here.
How do I get it back to the original? 1, 2, 3.
So it’s 4 times 10 to the negative 3.
Done. Ok. How about negative 68?
We said this would be the hard one. Don’t worry
about the negative until l- the end, and just
bring it down with you. Ok. So to the right
of the first non-zero digit. So we want it
Positive or negative? It’s
going to be positive, remember, don’t worry about the
negative, don’t think about the negative. Because that- that- the
absolute value of that number is greater than 1, so that’s going
to be positive. And then we have, we want it here, 6.8. But we know it’s- so
we want it here, but we know it’s really here. So it’s 1 place.
So it’s 6.8 times 10 to the first, but bring the negative down.
So do it as if the negative’s not there,
because think about that. If I check that, it’s going to move the
decimal to the right 1 place, and give me 68, which is where I started that problem.
At 68. So there we go. Alright ready for this one? Well-
what’s the deal with this one? This one already is between 1 and 10.
So, in scientific notation, I don’t want to move it at all,
that’s where the 10 to the 0 comes in. 7.6
times 10 to the 0 is that number in scientific notation.
Because it already is between 1 and 10. So know
where to move that. Ok? .43. .43 is going to be a
negative exponent, because it’s less than 1. Ok it’s going
to be a negative exponent. I didn’t even box that in.
Ok. Alright. It’s going to be a negative exponent.
And I- where do I want the decimal?
Well I want it as 4.3, I want it right there. But it was
here. So I have to move it 1 to the left. So it’s 4.3 times 10 to the negative 1.
by multiplying it. Putting it back in standard form.
And that’ll work out. Ok, here’s my most fun, you ready?
Alright. I’m actually going to move this
over so you can see it better, I’m just going to,
I’m going to erase this. Just to give me a little more space. Those
can stay on the board, for a second. And it’s .6 times 10 to the negative 2.
You actually have 2 choices. You want your choice number 1? Choice
number 1 is to just multiply this out first, because this is clearly
not in standard form, ok, bec- I mean sorry, not
in scientific notation. It’s not in standard form either.
But it’s not in scientific notation
because that’s not between 1 and 10. So you
have 2 choices. 1 choice is to multiply it out first.
First put it in standard form. And you would go 2
places to the left, so .006. And then take that number, and put it in
scientific notation. Ok. And if I did that, I’d want the decimal here,
so that would be 6, times 10, but I have to get it back to the original,
so it’d be negative 3. So I could do that. This might be a better choice, watch. And
when you do this, you’re using some other rules of exponents, so
this is why I like this kind of choice. Here we go.
What I see here is, I really need to put that in
scientific notation, so watch. I’m going to pretend that’s not there
for a second, and I’m going to go 6 times 10, we want the decimal right here.
We have to move it once to the left to get it back, so that’s negative 1.
Because my original number, .6,
is left- less than 1. But what do I already have there?
I already have there times 10
to the negative 2. Well what do I do with that? Well that’s
simple. That’s multiplication property. Keep the base, add the exponents.
Negative 1 plus negative 2 is negative 3. And that is, the same answer you
just got. So notice what I did, I wrote this in scientific
notation, pretended that wasn’t there. Put
that back in there, keep the base, add the exponents.
Pick your own poison, either way you
want to do it is fine with me. Ok? Now, I want you to take note of 1
other thing while we’re here, and this is in your workbook, is the fact that
it’s ok to have negative exponents. Scientific notation is
really pretty much one of the only places it’s
ok to have negative exponents. If you recall
before, when we had things like this- A to
the 1, B to negative 3- we moved them, to get them positive.
That was our goal then. Because it’s important
to have them positive with expressions. But scientific notation
is just another way to write really big and really small numbers.
So we have to have uh, a- a negative exponent,
if it’s a really small number. So they’re ok there.
Negative exponents are ok, but only
in scientific notation. Our goal, this is important,
our goal in scientific notation is to get
everything in the numerator. For instance, I could
write this, like this. Bring it down. But that’s not our goal.
Our goal in scientific notation is to have everything in the numerator.
So negative exponents are ok. Alright.
Because remember 2 factors, the 6 has a
positive exponent, that stays up. That has a negative
exponent, that would go down. But I don’t want to do that here.
I would do it with my variables, but not
with scientific notation. Let’s see why, as we continue.
Alright, I want to take a look at these, but
before we talk about how to do them, I want to talk about
how they’re similar. Or if they’re similar. You’re going-
pfft, they don’t look similar. But the truth is, they’re almost
exactly alike. Watch. Ready? Watch. Coefficient times base to an exponent,
times, coefficient times the same base to an exponent. Coefficient times base
to an exponent, times, coefficient times that same base to an exponent.
I just said the same thing!
Coefficient times base to an exponent, times,
coefficient times base to an exponent. Coefficient times
base to an exponent, times, coefficient times
base to the exponent. I said the same thing!
So, let’s talk about how we find the product. If you
know how to find the product of this, then you have to be able
to know how to find the product of this. So you ready? Ok. All you do here
is multiply the coefficients, we get 10. 5 times 2 is 10. Then Y times Y- Y to the
sixth times Y cubed, remember keep the common base, and we have a common base.
Add the exponents. And we get 9. 10Y to the ninth. Ok? So, we do
the same thing here. Multiply the coefficients, which
is 8.3, and this is on the next slide, you’ll see
in your workbook. 8.3 times 1.1, which is 9.13, ok. Times 10 to what power? Why- how
do I know it’s 10? Keep the common base, 10, add the exponents.
4 plus negative 2 is, 2. So we are done. Same,
same thing, ok. And that’s all you do
for multiplication with- uh, scientific no- notation.
So easy. And you’re saying, well,
wait, why don’t I just do this like, by hand? Or
by calculator? I have a calculator. So I have a big
number, why can’t I do the big number by calculator?
Because calculators only can display so many digits. This
is a, this is a better answer than your calc- well this is a not,
this, this would be easy on a calculator, because
it’s only, it’s not a big number. But if you had
really really big numbers, scientific notation is better.
Because it, it’s not as- as bad on the display. Ok. So we did
multiplication, let’s look at division. Alright, we’re going to
do division now. Now there’s 2 ways to handle division.
There’s everybody else’s way and my way. So,
method 1 is everybody else’s way. And you can- you- look at
method 1, the steps are right there for you, I’m going to do method 2.
And if you recall, there was a method 1 and
method 2 last time, and I liked method 2 as well.
Method 2 is the method I like here. So here’s what
I’m going to do. It’s very simple. First thing you do,
and in scientific notation, if you recall before, when
we had a division line with the uh, with the
letters, we really just simplified. Scientific
notation is different. You must divide, because you
want an actual answer. Well, luckily I picked really easy
numbers to divide. 8 divided by 4 is 2, and now here’s what
I’m going to do. I’m going to move- and
I’m allowed to move, I’m allowed to cross the
line because I have factors. I am going to move the
power of 10 on the bottom up. I’m always going to
move the power of 10 on the bottom up. Why
am I going to do that? I’m going to do that
because the whole point of scientific notation
is to get the answer in the numerator. So I
am not moving it because it’s negative. I am
moving it because I need my answer in the numerator.
So even if this was positive, I’d be moving it.
But, when you cross the line, you change
the sign of the exponents. It’s going to look like this, you ready.
I’m moving this up, and I’m going to get
times 10 because once you move it up now it’s attached
by multiplication- just like before. Instead of negative 3 it’s
positive 3. If that was a positive, when we moved it up it would become- negative.
Now I keep the base, add the exponents. And the reason
I do that, is because I’m afraid, a lot of times, that people will go
5 minus 3 is 2, when it’s really 5 minus a minus 3. Which is 5
plus 3, which is 8. Ok. So, I- you can do that, and that’s
fine, but I like to move it method 2. So I’m going
to deal with method 2. Ok, and that’s all you do.
Now I think we have enough information to answer
the challenge question. The NASA Data Archive at the Goddard Space
Flight Center contains 24 terabytes of data from previous
science missions. How many CD-ROMS does this
equal, if the capacity of 1 CD-ROM is approximately 6
times 10 to the eighth byte? Now, 1 terabyte is 10 to the
15 bytes, what the heck does this all mean? Here’s
what this all means, ok. I know I have 24 terabytes of data that
I want to get on CDs. I want to know how many CDs I need. Well
I know that 1 CD holds 6 times 10 to the eighth,
uh- bytes, of data. Ok. Bytes. Of data. Ok,
and I know 1 terabyte is 10 to the 15 bytes of data. So
first thing I have to figure out is how many bytes of data I have, total.
And then I can- then I have to figure out how many CDs I need to hold all
those bytes. So I know I have 24 terabytes, ok, but, 1 terabyte is 10 to the fifteenth. So I have to
multiply 24 times 10 to the fifteenth. And that’s what I get, when I multiply 24
and that looks really terrible. And that’s what I get when I
multiply 24 by 10 to the 15- teenth. That’s it.
I’m going to leave it like that, scientific notation.
So this is how- uh, actually it’s not scientific
notation yet, so hold on. But it is in, that’s what I-
how many bytes of data I have. Now, that’s how many bytes
of data I have. 1 CD-ROM holds 6 times 10 to the eighth bytes.
So I have to know how many CDs I want so
I have to divide. Ok, because I want equal
shares on all CDs. Now I know that this is not scientific
notation, but to be honest, I don’t care. I’m going to tell you why I don’t care.
When I’m dividing, ok, I can divide when
they’re not in scientific notation, and in the end I’m
just going to give you an answer that’s in scientific notation.
The reason I won’t change this now
is because sometimes, after you divide, your
answer is in scientific notation, that’s all you want anyway.
So you don’t have to change that to
scientific notation. Alright, remember we’re looking for how
many CDs we need. So this number is again not in
scientific notation but that’s ok, as long as our
answer is, at the end. So 24 divided by 6 is-
I’m going leave you a little bit more space
here- 24 divided by 6 is 4, times 10- and remember I’m going
to bring this up, that’s my method. I’m going to bring it up.
And when I bring it up, cross the line, change
the sign, we get 4 times 10 to the 7, CDs. Well that’s nice.
That’s a lot of CDs. How many CDs are- is it? Well now you can
leave it like that, but if somebody told me, I
want 4 times 10 to the 7 CDs, I mean, I- I- I’ve
never seen anybody say that. You probably want
this in standard form. In standard form that tells me I have
to multiply 4 by 10 to the seventh, or move the decimal 7 places to the right.
Or add 7 0s. 1, 2, 3, 4, 5, 6, 7. Ok. So that’s how many CDs I need. That’s
a ton of CDs, lots and lots of CDs. So that’s the end
of this question. So I can either leave it like
this, or like this. Doesn’t matter, but that’s how
you do that problem. Alright, these 2 are in your workbook,
there’s a multiplication, and there’s a division problem. You
try these, ok, and then we’ll- please try them. Stop the video,
try them yourself in the workbook, click the video
back, and we’ll go over them. Ok, we’ll do that in a minute. Ok, how do you think you did? How much
money would you bet on your answers? Alright here we go, we’re
going to multiply. 3.61 times 2.1, that’s what
we’re going to do first. Ok, and that’s 7.581.
Ok, keep the base. Add the exponents. Negative 18
and negative 31, is negative 49. So this is- now that’s a
huge number, you’d have to add 48 0s, can’t do that on the calculator.
Alright, so that one’s done. Alright
remember, negative exponents are ok. Take a look at this one. I
have to divide, so I’m going to divide 4.61 and 2, when I
do that I get 2.305, times 10. Remember what I’m going to
do, I’m going to bring this up. Cross the line, change the sign- of the
exponent, ok. And I get negative 3. Because negative 7 and a positive 4
is negative 3. And I am done here. There are 3 more examples
left, and the other 3, they’re just not
written in scientific notation. So what I’d like
you to do- don’t cheat, multiply them and put the
answer in scientific notation, that’s not what you’re supposed to do.
Put all the numbers in scientific notation,
and then do the problems. Ok, and then uh, click
back on when you’re ready. Alright, I’m hoping you didn’t cheat here.
Here we go. 70,000, that number’s bigger
than 1, it’s going to have a positive exponent. So it’s going
to be 7, because that’s where we want the decimal, and 1, 2, 3, 4.
So 7 times 10 to the fourth. Ok. Times,
this is going to be 1. Times 10- it’s going to be a negative
exponent because it’s less than 1- 1, 2, 3, 4. Negative 4. Ok, so that’s what we have there. Alright.
So we have 7 times 1 is 7, times 10 to the, 4 plus
negative 4 is 0. The answer to this problem is really just 7, ok.
7. So 7 times 10 to the 0 in scientific notation, in standard
form the answer is 7. You are done. Ok. Alright, take a look at this one.
Alright. We’re going to divide, we’re going
to put this is scientific notation. They’re both going to get negative
exponents because they’re both smaller than 0. And we have
9 times 10, because we want the decimal here, 1, 2, 3,
to the negative 3 power. Divided by 3 times 10 to the
negative, we want the decimal here, 1, 2, 3, 4 power. Right?
That’s it? First you put them in scientific notation.
Now I’m going to bring this up, because
that’s my method, right. Times 10 to the fourth.
Cross the line, change the sign- you’re not
bringing the number up, you’re just bringing the factor of 10 up.
9 divided by 3 is 3. 3 times 10 to the- I owe you
3, I have 4, so I have 1. So the answer there is
really just 30, because 10 to the first is 10.
3 times 10 is 30. So, in scientific notation it’s 3 times 10
to the first. In standard form it’s 30. Alright last one. These are both going
to be negative exponents. We want it after the 2, first non-zero digit.
1, 2, 3, that’s negative 3. This is 4 times 10 to the- negative, right? It’s a negative exponent.
We want it here, 1, 2, 3, 4. This is 2, 2 divided by 4. 2 divided by 4 is .5. .5, times 10, bring this up. It’s to the first again. Now, this
is not in scientific notation, or standard form. I’m going
to put this in scientific notation. Here’s what I’m going to do.
This is point, .5 would be 5. 5 times 10, remember it’s going
to be a negative exponent, assume that’s not there for a minute. Ok.
To the negative 1. But there is a 1 there. So it’s 5 times 10 to the 0.
So the answer to this question is 5 times 10 to the 0, or just
plain 5. Ok, and you’re done. So the goal is to first write them in scientific
notation, and then to work them out in scientific notation. And in the end
you can either leave your answer in scientific notation, or put it
in standard form, that’s up to you unless your directions
give you a- give you uh, some way to have the answer.
But either way is fine with me. Alright.