Learn Metric Units & Unit Conversions (Meters, Liters, Grams, & more) - [5-8-1] - Free Educational videos for Students in K-12

Learn Metric Units & Unit Conversions (Meters, Liters, Grams, & more) - [5-8-1] - By Math and Science

Transcript


00:00	Hello . Welcome back . The title of this lesson
00:02	is called metric unit conversions part One . So in
00:06	this lesson I'm really excited to teach you because we
00:09	are going to be learning about what the metric system
00:12	is reviewing some of the units that we've talked about
00:14	in the past will be specifically converting from one unit
00:17	to another . And we will be doing it using
00:19	my method which is using a unit conversion kind of
00:23	table . Which will also help us as we go
00:25	into more math classes down the road , it really
00:28	is one of the most important things that you can
00:31	learn in math is how to convert units because we
00:34	use it in physics . We use it in chemistry
00:36	. We use it of course in math and we
00:38	use it in every branch of science and engineering .
00:41	All right . So before we get too far let's
00:43	just review and talk about what these uh metric unit
00:47	conversions are . So in general we're going to be
00:49	talking about length , units of length , units of
00:53	mass and units of volume . And before I go
00:55	any farther and actually talk about any of this stuff
00:58	. I want you to look at the numbers in
00:59	the tables . Forget about what they mean and what
01:01	they mean doesn't matter . You have ones 1000 110,000
01:06	. You see all of these numbers are with one
01:09	and some zeros at the end there . So that's
01:11	called a power of 10 . Power of 10 is
01:14	10 . It's 100 it's 1000 . It's 10,000 .
01:17	It's 100,000 things like that . You can see that
01:20	all of the metric system involves Nice numbers , powers
01:24	of 10 . Now in the future we're going to
01:27	be talking about the US system or the british system
01:29	of measurement and converting between pounds and ounces and things
01:33	like that . And when I show you the same
01:36	table , uh the numbers will not look nice like
01:39	this . They'll look weird and just random . And
01:41	that is one of the main reasons we use the
01:43	uh , the units of the metric system in science
01:46	and engineering is because all of the numbers are very
01:49	nice and they're very simple to work with . All
01:51	right now , first we want to talk about unit
01:53	of length and then we're gonna go from there .
01:56	So what is the unit of length in the metric
01:58	system ? The basic unit of length . You can
02:00	see it in red here is the meter . This
02:03	is the basic unit of length . We're gonna come
02:05	back to what ? The unit of length of a
02:08	meter . You know how you work with it later
02:10	. But for now just remember the basic unit of
02:11	length is called the meter . Then we talk about
02:15	something called mass . The unit of mass In the
02:18	metric system is called the graham . You see it
02:20	is in red here . The basic unit here we
02:22	call it the graham . Um At least in this
02:25	lesson , we're gonna call it the graham . The
02:27	paperclip that I'm holding up is one g . And
02:31	the basic unit of one m is the stick here
02:34	. All right now , exactly what is mass .
02:37	Some people think it's the same as weight . It's
02:39	not really the same as weight . The unit of
02:41	mass of grams is telling you how much material is
02:44	in here . It's kind of telling you how many
02:46	atoms and what kind of atom it's it's how much
02:49	mass how much matter is inside of this thing .
02:52	Now if I take this paper clip to the moon
02:54	, it will not weigh as much but it will
02:56	still have the same mass . If I take it
02:59	to jupiter , it will not weigh as much but
03:01	it will still have the same mass . If I
03:02	take it to Neptune it'll it'll will not weigh the
03:05	same but it will have the same mass . So
03:08	the mass of an object never changes . But when
03:11	you go to different planets with different strength gravity ,
03:13	the force of gravity , the weight can change but
03:16	the mass never change . The basic unit of mass
03:18	is a gram . And then finally we have the
03:21	unit of volume , unit of volume . It doesn't
03:23	talk about how much matter is in there . It
03:26	talks about how much space something occupies , How much
03:29	space in our world does it take ? The unit
03:32	of volume is the basic unit of volume in the
03:34	metric system is called the leader . And this right
03:37	here is one leader here . So if you can
03:39	kind of imagine drinking something like this , this is
03:41	one leader . All right . So those are the
03:43	three main units that we're going to be talking about
03:45	. Now let's go a little more detail here .
03:47	You see this chart . We have meters meters meters
03:50	. All right . We have to learn a little
03:51	bit more . You see we have kilometer kill .
03:54	Oh , the prefix kilo means 1000 of something .
03:58	So one kilometer is just 1000 of these things called
04:02	meters kilo means 1000 . So it's very simple .
04:05	You see , one kilometer is 1000 of these meters
04:08	, right ? one kg is just 1000 of these
04:12	little grams , which are which are these smaller units
04:15	the size of the amount of mass in this paper
04:18	clip , one kg is just 1000 of these things
04:22	. One kilometer is 1000 of these meters . So
04:25	what do you think a kilo liter will be ?
04:28	It's just going to be 1000 of these leaders .
04:31	So it's very easy to talk about small and large
04:34	numbers in the metric system by using the prefixes .
04:37	If I tell you I have two leaders , you
04:40	know , it's something you can hold in your hand
04:42	. Right ? If I tell you I have to
04:44	kill a leaders , then you know it's 2000 leaders
04:47	because kill , oh , means 1000 . And so
04:49	you can easily talk about sizes of things just by
04:52	the word . So that's killer . Killer means 1,000,000
04:55	m , kilogram 1000 g . Kill the leader .
04:57	1000 liters . Alright , Now let's talk about um
05:01	, the the prefix Cynthia when you see Santa ,
05:05	what does it mean ? It doesn't mean what a
05:08	lot of people think it means , simply means 100
05:11	times smaller . So when I say I have a
05:14	centimeter , it means I have something 100 times smaller
05:18	than a meter . You see , killer means 1000
05:21	times bigger than a meter . And sensing means 100
05:24	times smaller . So on my meter stick here on
05:28	my meter stick , see here's a meter from all
05:30	the way here to here is a meter , but
05:32	if you look closely , you probably can't see it
05:33	on the camera . This meter stick is divided into
05:36	100 markings that go all the way to the end
05:39	. Here's 40 50 60 70 80 and you have
05:42	the numbers in here and the 90 and then 100
05:44	. So if you take this meter stick and chop
05:46	it into 100 little pieces . One of those little
05:49	pieces about the width of my finger , the width
05:51	of my finger here is called a centimeter centimeter is
05:55	100 times smaller than the base unit . Everything is
05:59	related to the base unit here is a meter centimeter
06:02	is 100 times smaller now because centimeter is 100 times
06:06	smaller . It takes 100 of these little bitty centimeters
06:09	to make one m . That's what this is showing
06:11	you . 100 of these little centimeters . Makes one
06:15	m . Now , if that's what's happening for length
06:17	, what do you think is happening in terms of
06:19	mass grams ? Remember the basic unit of mass .
06:23	Is this paperclip a gram ? So if I have
06:26	uh something called a cent to graham , it's 100
06:29	times smaller than this little thing , right in mass
06:33	. So it's gonna take 100 sent to Graham's to
06:36	be the same as one g . Because these center
06:38	grams are tiny , tiny tiny there 100 times smaller
06:40	than this . So , it takes 100 of these
06:42	center grams to make one g . Same thing for
06:45	leaders . 100 sent to leaders . I need 100
06:48	of these tiny little center leaders to equal one leader
06:52	. Remember the prefix ent means 100 times smaller .
06:55	All right . And then the last one , last
06:58	big one we're gonna talk about is millimeters . I
07:00	know everybody's probably heard of millimeters . So what does
07:03	million mean the prefix . Million means 1000 times smaller
07:08	. Right ? So one millimeter is tiny . Think
07:11	of millipede . Think of santa pd even right Centipedes
07:14	. 100 times smaller millipede . Uh , is 1000
07:18	times smaller . So you there's no way you're going
07:20	to see this on the camera . But if you
07:22	get an actual meter stick , there's little bitty marks
07:25	across the top that you're not gonna be able to
07:27	see on screen , but I can see them here
07:29	. And there's 1000 of these little markings that go
07:31	all the way from here to here . So 1000
07:33	of these tiny , tiny millimeters will equal one m
07:37	. And 1000 of these tiny tiny milligrams is the
07:40	same as one g . And 1000 of these tiny
07:43	tiny milliliters is the same as one leader . So
07:46	the main thing I want you to pull out of
07:48	this is the base unit of length is this thing
07:51	called a meter . And when we have a kilometer
07:53	, it's 1000 times the length of this . Because
07:56	the killer means 1000 times bigger . Right ? And
07:59	then we have kilogram 1000 times of a gram and
08:03	then kill a leader , 1000 liters . So ,
08:05	Killer means 1000 uh , times larger than whatever the
08:09	base unit is , millie means 1000 times smaller .
08:13	So it takes 1000 of these millimeter millimeters to equal
08:16	a meter . It takes 1000 of these milligrams to
08:19	equal a gram . It takes 1000 of these milliliters
08:22	to equal a leader . And then for senti it's
08:24	100 times smaller . So it takes 100 of these
08:27	centimeters to equal a meter , which are these markings
08:30	. The width of my finger is a centimeter and
08:32	it takes 100 of these center grams to equal a
08:34	gram . And it takes 100 of these centimeters to
08:37	equal a liter . And then I have one more
08:39	up here that we also use quite a bit as
08:41	well . And that is that . One centimeter is
08:43	10 millimeters . And you can see that on there
08:45	. If you if you look at a centimeter on
08:48	a meter stick , you can see that there's 10
08:50	little millimeter markings between there . So this one here
08:53	is kind of separate from the others . That one
08:55	centimeter is equal to 10 of these smaller things called
08:59	millimeters . So now that we have all of that
09:02	kind of background out of the way , we're ready
09:04	to start solving our problems Alright , for our first
09:08	problem , I want to start off with a unit
09:11	of five g . Five G means five g .
09:14	And I want you to convert that to some number
09:17	of milligrams . Now , a lot of students ,
09:20	when they look at something like this , they just
09:22	freeze up and they don't know what to do .
09:24	The very first step is to know I want to
09:26	go from grams to milligrams . And if you don't
09:28	remember then go back to the table , we go
09:31	down to mass and we're looking at Graham's and milligrams
09:34	. So here's grams and here's milligrams . So if
09:37	you don't remember then you just look at the table
09:39	. one g is the same as 1000 of these
09:41	tiny tiny things called milligrams because of milligram is 1000
09:45	times smaller than a gram . So to get one
09:48	g , I need 1000 of these tiny tiny things
09:50	to get there . So one g is 1000 mg
09:54	. Now , what you need to do is figure
09:56	out a way to multiply or divide to make this
09:59	thing work . This is how I want you to
10:00	solve every unit conversion problem . I want you to
10:03	write down what you have been given five g ,
10:06	draw a line under it and draw a vertical line
10:09	next to it . And right here I'm going to
10:11	write down one g is 1000 mg . Now ,
10:16	the way I'm going to write it down and I'm
10:17	gonna put one g on the bottom and 1000 mg
10:22	milligrams . This thing right here is the conversion factor
10:25	one g 1000 mg . That comes straight off my
10:28	chart . Now I could write it like this ,
10:31	I could flip it over and write it upside down
10:33	. But we are going to see in a minute
10:34	why we're writing it this way when we write it
10:37	this way with a gram on the bottom and the
10:38	graham on the top , the grams cancel each other
10:42	. The reason the grams cancel each other when they're
10:44	on the bottom and the top is just like fractions
10:46	. When you have uh a zero on the top
10:51	and a zero on the bottom of a of a
10:53	of a fraction . That has numbers . You can
10:55	cancel the zeros because basically what you can think about
10:58	doing is you can divide the top by grams in
11:01	the bottom by grams and it gets rid of them
11:03	. Just like any fraction . You can divide top
11:05	and bottom by whatever you want to get rid of
11:08	it . I can divide this by grams and this
11:09	by grams and it will get rid of the grams
11:12	. An easier way to think of it is if
11:13	you see grams on the top and on the bottom
11:15	you just get rid of them . Now the only
11:17	unit I have left is milligrams . So what this
11:19	is telling me is that to go from here to
11:21	here I need to take the five multiply by 1000
11:26	and then divide by one . Everything on the top
11:28	gets multiplied and everything on the bottom . You divide
11:31	by that . So what is five times 1000 ?
11:35	Well the easiest way to think about that , you
11:37	can write it down five times 1000 but just cover
11:40	up the zeros five times one is five . And
11:43	then since I covered up the zero is I have
11:45	to add the zeros back in . So it's 5005
11:48	times 1000 is 5000 . The only unit left is
11:51	milligrams . And I've divided by one here , which
11:54	doesn't change anything . So what I've done is I've
11:57	taken five times 1000 and then I divided by one
12:00	. Now I could go down here and right five
12:02	times 1000 and do it all . But I'm trying
12:04	to also show you how to multiply and divide by
12:06	powers of 10 . When you multiply by a power
12:10	of 10 , meaning you multiply by 10 or 100
12:13	or 1000 or 10,000 or 100,000 . Then it's very
12:17	easy because all you do is ignore the zeros five
12:20	times one is five and then you add the zeros
12:22	back in . So when you multiply by powers of
12:25	10 , it's very simple . You just add the
12:26	zeros at the end . When you divide by powers
12:29	of 10 , we'll see what we do here in
12:30	just a minute . But for here we're telling ourselves
12:33	that five g it's 5000 mg . Does that make
12:36	sense ? Well , I know here that one g
12:40	is the same as 1000 mg . So if I
12:43	have five of these grams I must have 5000 of
12:46	these milligrams . And that is the final answer .
12:49	As we go through these problems , I'll be able
12:52	to do less and less and less talking . But
12:55	here in the beginning I just want to make sure
12:56	everybody's on the same page . Next problem , Let's
13:00	say I have 6000 l and I want to convert
13:05	that to kill the leaders . Killer leaders . So
13:09	I need to go between leaders and killer leaders .
13:11	So let's go back to our chart and think about
13:13	it . We're looking at leaders and we're looking at
13:15	leaders and killer leaders . Now this is telling us
13:18	that one . killer leader is the same as 1000
13:20	liters . Now I'm using my chart but actually once
13:23	I start learning , I don't really need the chart
13:25	because I know that kill oh means 1000 times bigger
13:29	. So one killer leader must be 1000 of these
13:32	leaders . So one kill a leader is 1000 L
13:37	. Now how do I arrange it ? I first
13:39	write down what I know . 6000 leaders draw a
13:42	horizontal line and then draw a vertical line . Now
13:45	I know that one killer leader is 1000 leaders .
13:49	Now I could put the killer leader on the top
13:51	or the killer leader on the bottom . The way
13:53	that you need to write it . Is that one
13:55	Killer leader is 1000 liters . Why do I write
14:00	it this way ? I could flip it over and
14:02	have the killer leaders on the bottom and then the
14:04	1000 liters on the top . But if I do
14:06	that , nothing will cancel . You see it only
14:09	cancels . If I have something on the top and
14:11	something on the bottom Leaders will cancel with leaders .
14:13	If I flipped it over , nothing would cancel .
14:15	I would have killer leaders here and that would be
14:17	wrong . So what is this telling me that I
14:19	need to do ? It's telling me that what I
14:22	need to do is take 6000 and multiply by one
14:26	. Everything on the top gets multiplied once I do
14:29	that , then I divide by everything on the bottom
14:31	. So what am I going to actually have ?
14:33	6000 times one on the top of 6000 And then
14:37	on the bottom I still have to divide by 1000
14:40	. So here I have kind of a fraction 6000
14:43	over or divided by 1000 . So you can do
14:46	the long division . You can write down 6000 .
14:48	Put your division , house divide by 1000 . You
14:51	can do all that . Or you can listen to
14:53	what I'm telling you about . Multiplying and dividing by
14:56	powers of 10 . Because here I have 6000 on
15:00	the top And I have 1000 on the bottom .
15:04	And when you're dividing numbers like this , if I
15:07	have uh something on the top and the bottom I
15:10	can cancel . So any time you have zeros in
15:14	the top zero is in the bottom . I can
15:16	cancel this zero with this one . This zero will
15:18	cancel with this one . This zero will cancel with
15:21	this one . And what will I actually have left
15:24	? I will have a six on the top and
15:26	divided by a one on the bottom . And so
15:28	the answer will be six . And the only unit
15:30	I have left because the leaders cancel what the leaders
15:33	is kilo leaders . Now let's see if this makes
15:37	sense . We know that one killer leader is 1000
15:41	liters . So if I were to have six of
15:43	these killer leaders , it should be 6000 liters .
15:46	And so this unit conversion makes sense . Now before
15:48	I go to the next problem , I want to
15:50	explain why this is okay . Why can we strike
15:52	zeros like this ? The reason is because this is
15:54	a fraction , it's division . But we're writing it
15:56	as a fraction 6000 divided by 1000 or 6000 over
15:59	1000 . I can simplify fractions by dividing top and
16:03	bottom by anything I want . So if I take
16:05	and take this top and divided by 1000 and then
16:08	take this bottom and divided also by 1000 6000 ,
16:11	divided by 1006 . 1000 divided by 1000 is one
16:15	. So striking , the zeros is the same thing
16:17	as simplifying fraction , Divide by 1000 divided by 2000
16:20	. And you can certainly do it that way if
16:21	you want . But I'm trying to teach you to
16:23	strike through the zeros because we're going to be doing
16:26	that a lot more when we get into algebra and
16:28	pre algebra and other kind of other parts of math
16:31	later . So that is in a nutshell . Why
16:34	unit conversions of metric system is so easy . Why
16:37	the metric system is so much better ? Because when
16:39	I multiply this , I just it's very easy to
16:41	multiply when I divide these , it's very easy to
16:44	divide . All right , let's take a look at
16:46	the next problem . One centimeter is equal to or
16:49	let's convert one centimeter into how many millimeters . Right
16:53	? One centimeter . Warning from centimeter two millimeter .
16:56	Now , actually , if you look at our chart
16:59	, I already wrote down that one centimeter is 10
17:01	millimeters . So we already know the answer . What
17:03	we wanna do is prove to ourselves that this is
17:05	true . So let's go ahead and do that .
17:08	Here . What we have Is we can write down
17:12	what we are given . We have one cm And
17:16	we want to do is try to find a conversion
17:18	factor that goes from cm two . Now here we
17:22	actually already have it . We already we already have
17:24	the answer . We know that this is the answer
17:26	, but we want to show and prove to ourselves
17:28	without using that . So instead of going straight from
17:31	centimeters two millimeters , is there any other way I
17:34	could get to the answer ? Well I could go
17:36	from centimeters to meters and then once I met meters
17:40	I could go from meters , two millimeters . So
17:42	you can do these conversion steps and jumps . All
17:46	you have to do is jump through the tables from
17:48	one unit to another . All right . So if
17:51	I want to go from centimeters to meters , I
17:53	know that there's 100 of these centimeters in one m
17:57	. So I'm gonna write it down like this one
17:59	. I'm sorry . Uh , 100 of these cm
18:03	are in one of these meters now . Why am
18:06	I writing it down this way ? Because if I
18:08	flip it over with cm on the top and meters
18:10	on the bottom , nothing will cancel . But this
18:12	way , the cm here will cancel with the cm
18:15	there . Now , if I stop the the conversion
18:18	here , if I just do the calculation , I'm
18:20	gonna end up in meters . But I don't want
18:22	to go two m . I want to go to
18:23	millimeters . I know that one m is 1000 of
18:27	these little bitty mila meters . I have to put
18:29	the one m on the bottom and 1000 millimeters on
18:33	the top . Why am I writing it this way
18:35	? Because if I write it this way , I
18:37	have this meters canceling with this meter , If I
18:40	flip it over With 1000 on the bottom , nothing
18:43	will cancel . So this is the only way to
18:45	make sure that everything cancels and all I have left
18:48	is mm . That's where I want to go now
18:51	. How do I figure out the answer ? I
18:53	have to multiply everything on the top and then divide
18:56	by everything on the bottom . So here I have
18:57	one times one is one . Uh , and then
19:00	one times 1000 on the top will be what ?
19:03	1000 ? So I'll have 1000 on the top .
19:06	And on the bottom I'll have 100 have to multiply
19:09	everything on the bottom of 100 . Times one is
19:10	100 . So what I have is 1000 on the
19:14	top and 100 on the bottom . So 1000 on
19:17	the top and 100 on the bottom . Remember I
19:20	told you the same thing , if you have trailing
19:23	zeros like this , this zero can cancel with this
19:25	one . This zero can cancel with this one .
19:28	The answer that I get on the top is a
19:29	10 and on the bottom is a one and 10
19:32	divided by one is 10 in the unit is millimeters
19:36	. Yes . And what we're saying is that one
19:39	centimeter is 10 millimeters , one centimeter is 10 millimeters
19:43	. So we've proven that what is in this chart
19:45	is correct , but not by using this line by
19:47	using everything else . And so what we did is
19:51	we said , well one we go from centimeters to
19:53	meters and then we go from meters , two millimeters
19:57	. And then we multiply everything on the top ,
19:59	multiply everything on the bottom and then we do this
20:01	division . But when we divide with trailing zeros like
20:05	this we can cancel the trailing zeros and then it
20:07	makes everything simple . I don't have to do any
20:09	like super hard division because dividing by 100 is really
20:12	really easy . Right , last thing I'll say is
20:16	you can think of this two ways you can think
20:17	of it as multiplying the tops , multiplying the bottoms
20:20	and then dividing or you can think of it as
20:22	one times one is one , Then divide by 100
20:25	, then multiply by 1000 , then divide by one
20:29	. So it's it's the same thing , it's just
20:31	in a different order . So one times one is
20:32	one . If you divide by a by 100 1
20:36	divided by 100 . If you do the long division
20:38	you'll get a decimal . If you take that and
20:40	then multiply by 1000 then you'll get the answer .
20:43	But doing it this way is easier . If you
20:45	multiply the tops and multiply the bottoms , then you
20:48	get to the answer because you can cancel these things
20:50	much much faster and much much easier . Alright with
20:54	more practice comes Many more skills . So let's continue
20:59	along . What about three killer leaders ? Let's go
21:02	to milliliters . So we want to do is write
21:06	down what we have been given three kill Oh leaders
21:10	. Now we want to try to find a conversion
21:12	that goes from killer leaders , two ml , that's
21:15	Killer Leaders leaders . There's no conversion that goes from
21:18	Killer leaders directly to milliliters , so we can't do
21:22	that . Is there another path to the answer ?
21:24	We can go from killer leaders to leaders And then
21:27	from leaders , two ml . So we do it
21:29	in two steps . So we know that one killer
21:32	leader is 1000 liters because kilo means 1000 . So
21:35	one kill a leader . We write it down on
21:37	the bottom is 1000 liters . We write it down
21:41	this way because this is the only way killer leaders
21:44	cancels . If we stop the calculation here , we'll
21:47	just get leaders . But we don't want leaders .
21:49	So we continue . We go from leaders , two
21:51	ml , leaders to middle leaders . One leader is
21:55	1000 ml . Okay , we're at one leader on
21:58	the bottom , 1000 ml on the top . Now
22:04	leaders cancels with leaders . We wrote it this way
22:07	. If we flipped it over , nothing would cancel
22:09	. We have to write it this way to make
22:10	it canceled . And so everything is canceled . Except
22:13	now we have the unit at the end that we
22:15	want . The reason we're doing all this by the
22:17	way is because it's hard to know how do I
22:19	multiply or do I divide by these conversion factors in
22:22	this way of doing it Makes it very easy .
22:25	You don't have to guess . You always know what
22:27	to do because this is the only way that it
22:29	can be written down to get the right answer .
22:31	How do I finish it ? Well I say I
22:35	have on the top three times 1000 and then have
22:38	to divide by one . That's not gonna change anything
22:40	and then multiplied by another 1000 then divide by one
22:42	. That's not gonna change anything . So the dividing
22:44	by the ones isn't really going to do anything .
22:46	So three times 1000 is 3000 . Right ? So
22:51	what I have here is 3000 . But I still
22:54	have to multiply by another 1000 . Mhm . Now
22:57	how do I do this ? Of course I can
22:58	write it all down and do all along the long
23:01	multiplication . But I know that when I multiply by
23:04	a power of 10 , all I have to do
23:06	is write down its cover up , essentially cover up
23:10	the zeros here . I'm multiplying by one , so
23:12	I'm gonna get 3000 and then I'll just add the
23:14	zeros back in three more of them . And so
23:17	it's going to be three million . And the unit
23:18	here is Millie leaders . So the unit is three
23:22	million ml . Another way to look at it is
23:26	I can multiply this and three times one is three
23:29	and I add three zeroes to the end and then
23:31	I take that and multiply by 1000 . Again multiplying
23:35	by one , so that makes it 3000 . And
23:38	then I add the zeros and again . So basically
23:40	when you multiply by 1000 you just kind of cover
23:42	up the zeros , multiplied by one and then add
23:45	the zeros back in at the end . That's all
23:46	you're doing . So that's why there's six zeros here
23:48	because there's six zeros throughout here . Now , does
23:50	this make sense ? Let's see if this actually makes
23:53	sense . Were saying three km is three million ml
23:58	. Okay , three killer leaders is 3000 of these
24:02	leaders and every one of these leaders has 1000 of
24:06	these milliliters . So it makes sense that 3000 of
24:09	these of these leaders would yield a huge number of
24:13	milliliters . And that is exactly what we found .
24:15	Uh All right , let's move right along . Yeah
24:20	. To problem number five . What about 42,000 mm
24:27	? And let's convert that two m . So ,
24:29	first we write down 42,000 millimeters And we want to
24:34	convert that two m . Now , let's think about
24:36	it . Can we figure it out without looking at
24:38	the chart ? Well , Millimeter Millie means 1000 times
24:43	smaller . So if I'm going from millimeters to meters
24:46	, I think there's 1000 of those little bitty millimeters
24:49	in a meter . Let's see if we're right .
24:52	1000 millimeters is equal to one m . That's the
24:56	conversion factor we want to use . And the only
24:58	way we can write it is 1000 on the bottom
25:01	millimeters is one m . That's the only way it
25:05	works . Because if we write it upside down ,
25:07	we won't cancel anything here . We cancel millimeters .
25:11	And so we have 42,000 times one and we have
25:14	to divide by this . So let's write it .
25:16	We multiply the top , we're still gonna have 42,000
25:20	. And on the bottom we have 1000 . Right
25:23	? And so what do we get ? We can
25:25	cancel this zero with this one . This canceled with
25:27	this one . This cancels with this one . What
25:29	do I get ? 42 on the top , divided
25:31	by one on the bottom . And so the answer
25:34	I actually get is 42 in the unit left over
25:38	is m . So the answer is 42 m .
25:42	Alright , cruising right along making a little more progress
25:47	. Now that we know what we're doing . 800
25:50	cente grams . Let's convert that to milli grams .
25:54	Now I don't have a conversion that goes straight from
25:56	center grams , two mg . Right ? But I
26:00	do have something that goes from center grams , two
26:02	g . And then once I'm in grams I can
26:04	go from grams to milligrams . So that's what we
26:07	want to do . We want to do it in
26:08	two steps . 100 centre grams is one g .
26:12	So let's first write down what we know . 800
26:17	cinta grams Hopes not cm . sent two g santa
26:23	grams . And we just said that 100 of these
26:26	little Cinta grams is one g . Right ? And
26:31	we have to write it like that . Because that's
26:32	the only way that cinta grams will cancel . If
26:34	we stop , the calculation will be left with grams
26:37	. But we don't want to stop there . We
26:39	want to go from grams to milligrams . one g
26:42	is 1000 mg . So we continue our table .
26:48	We can string them along and we say that one
26:50	g is 1000 nearly ramps . And then by arranging
26:56	it like this , if we flip it over ,
26:57	nothing will cancel arranging it . Like this means grams
26:59	cancels with grams . Now , how do we complete
27:02	the calculation ? Well , first we multiply the tops
27:07	, right ? And by multiplying the tops . We
27:09	have 800 times 1000 times one . But that doesn't
27:12	do anything times 1000 . But it's easy to multiply
27:15	that we just cover up the zeros . Multiply by
27:17	one . We get 800 then we have to add
27:21	the zeros back in three more of them . So
27:23	this is what happens when we multiply the top .
27:25	We have to divide by this . But this times
27:28	one is still 100 . So it's just gonna be
27:30	100 on the bottom . Now we have a lot
27:33	of trailing zeros . This can cancel with this and
27:35	this can cancel with this . And so what's going
27:38	to happen on the top ? I still have 30
27:41	. So that's 8000 Divided by the one that's on
27:45	the bottom . And so what you have is 8000
27:48	. What are we talking about ? Milligrams ? That's
27:50	the only unit left me check and make sure that's
27:53	right . 8000 mg . So you see why ?
27:55	It's so nice to work with the metric system because
27:58	multiplying when you have a bunch of Zeros , makes
28:01	it easy to multiply and then dividing . When you
28:03	have a bunch of Zeros , makes it easy to
28:04	divide . And since everything is a power of 10
28:07	, it just makes it very simple . We have
28:08	a couple more problems . I want to erase this
28:10	and continue our lesson . All right . Only two
28:13	more problems . Let's take a look at 51,000 millilitres
28:18	. Let's convert that into the unit of leaders .
28:22	Well , the first thing is we write down what
28:23	we are given were given 51,000 millilitres and we want
28:28	to find a conversion factor that goes to Leaders .
28:31	All right . We think there is one . So
28:32	we go back and check our table and we see
28:36	that we have millilitres and litres here , one liter
28:38	is 1000 of these little bitty milliliters . So we
28:41	know that one leader is 1000 mL . The only
28:45	way we can write it is with one liter on
28:47	the top and 1000 mL on the bottom . Because
28:50	if we flip it over , nothing will cancel .
28:53	This is the only way the milliliters cancel leaving us
28:56	with leaders . So all I really have to do
28:58	is take the 51,000 times the one which is just
29:01	gonna be 51,000 and on the bottom I just have
29:04	1000 . And now I have to do this division
29:08	but I have a lot of trailing Zeros . This
29:10	cancels and this cancels and this cancels . And all
29:13	I really have on the top is 51 and on
29:15	the bottom I just have a one . And so
29:17	that's divided by one . So it's 51 . What
29:20	? Leaders ? And the answer is 51 leaders .
29:23	And that's the final answer . Here's our last problem
29:27	for this lesson . We have 19 kg . Let's
29:31	convert it to send two g kilograms to center grams
29:36	. We do not have a direct path from kilograms
29:38	to Cinta grams , but we do have a path
29:41	from kilograms . two g . And then once we
29:44	get two g we go from grams to Cinta grams
29:46	. So let's start by saying one kg is 1000
29:48	of these little bit of grams . That's right down
29:53	what we are given 19 kilograms , extend our table
29:59	And we want to write down now that one kg
30:03	Is 1000 of these little bitty g . We have
30:06	to write it that way because it's the only way
30:08	the kg cancelled now going from grams to Cinta grams
30:12	. Let's remind us what that is . one g
30:16	is 100 of these . Little bitty center grams .
30:20	Right ? So we go and say , well one
30:23	g is 100 cinta grams . This is the only
30:27	way I can write it because I have to have
30:29	a gram on the top and graham on the bottom
30:31	to cancel . Now I am left with the unit
30:33	. I want to calculate . So how do I
30:36	finish the calculation ? Have to multiply the top and
30:38	then I divide by the bottom . But one times
30:40	one is one . So divided by one is going
30:42	to do nothing . So really , I just have
30:44	to multiply the top . So here I have 19
30:47	times 1000 . What is that ? Well , you
30:50	just cover up the zeros 19 times one is 19
30:54	. And then I just add the three zeroes .
30:56	And then I still have to multiply by this 100
30:59	. What is this times 100 I just cover up
31:01	the zeros , multiplied by one . It's gonna be
31:04	19,000 and I covered it up here and I have
31:08	to add the zeros back in . So I had
31:10	to more zeros at the end . So here's a
31:11	comma and then here's a comma , 1,900,000 . And
31:16	the unit I'm talking about is sent to rams .
31:19	So you see multiplying by powers of 10 , I
31:21	just multiplied by one , add the three zeroes and
31:25	then I multiplied by this one . I multiplied by
31:27	one and then add the two zeros at the end
31:30	. So basically when you multiply by 10 or 100
31:32	or 1000 you just essentially write down what you start
31:36	with and you add zero Xanthi . And it's it's
31:37	very simple and that's why unit conversions in the metric
31:40	system is so , so convenient when we get into
31:43	science and engineering and astronomy and things like that ,
31:48	we only use the metric system because this table ,
31:51	remember in the beginning I told you this entire table
31:54	, all it has is tens and hundreds and thousands
31:57	and things like this and it makes it very easy
31:59	to calculate . So I want you to practice every
32:02	one of these problems really want to make sure you
32:05	understand how to set these tables up and how to
32:08	know what to do . The whole reason we're doing
32:10	this table is because if you're trying to go from
32:12	kilometers , two mL and you don't do it this
32:15	way , then you're going to find yourself not sure
32:18	what to do with the conversion factors here . You're
32:20	not gonna be sure if you should multiply or divide
32:22	, it's going to be hard for you to figure
32:25	it out what to do . But if you just
32:27	put down what you're given and then write each conversion
32:30	in a way that gets you down to where you're
32:32	trying to go , then the table tells you if
32:34	you should be multiplying or dividing and you will always
32:37	get the right answer . And as we move into
32:39	chemistry and other classes later , we're going to use
32:42	all of this in every single problem . So this
32:45	stuff you're learning , you'll use it for years and
32:47	years and years , so I'd like you to practice
32:48	it . Follow me on the part two , we'll
32:50	get a little more practice .

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