Learn Metric System & Unit Conversions - Dimensional Analysis - Math, Physics, Chemistry - [16] - Free Educational videos for Students in K-12

Learn Metric System & Unit Conversions - Dimensional Analysis - Math, Physics, Chemistry - [16] - By Math and Science

Transcript


00:0-1	Hello . Welcome back . We're working on converting metric
00:03	units of length . So we're talking about meters centimeters
00:07	millimeters kilometers . That's what we're working on now .
00:10	And so we've been using these conversion factors that I
00:12	want to call your attention to . But as we
00:14	talk about these conversion factors , I want you in
00:16	your mind to have what a meter looks like .
00:18	The length of a meter is the length of this
00:20	stick . Right ? If you have 1000 of these
00:23	meters , this meter is the basic unit of length
00:26	in the metric system . It's what we call the
00:27	base unit . 1000 of these things . 1000 times
00:31	larger than this is what we call a kilometer .
00:34	Right ? If you take this base unit and instead
00:37	of 1000 times larger , look at 1000 times smaller
00:40	than it . Then you have what we call a
00:42	millimeter , which is a tiny marking on here .
00:44	A millimeter is about the width of a pencil strike
00:47	on a page , right ? 1000 times smaller than
00:50	a meter . Is what we call a millimeter millie
00:52	means 1000 times smaller . Kila means 1000 times larger
00:57	. So a kilometer is a really long distance .
00:59	You drive it in a car . A millimeter is
01:01	1000 times smaller than this thing . And so it's
01:05	a very small unit . And then we have the
01:07	unit of a centimeter , that's the width of my
01:09	finger , roughly on the stick . With these little
01:11	markings here and center means one that 100 times smaller
01:17	. So we have the basic unit here . We
01:19	have 100 times smaller than this means we have 100
01:21	of these centimeters that fit in a meter . 1000
01:24	times smaller than a meter means we have 1000 of
01:27	these millimeters that fit in a meter . And then
01:30	we have 1000 times larger than this , which we
01:33	call a kilometer . So now that we have the
01:37	basic understanding of our unit conversions here . And of
01:39	course we also talked about cm and 10 fit into
01:43	a centimeter as well . Let's continue converting . Let's
01:46	take a look at something like six m . Let's
01:49	convert it to mm . Right ? So the first
01:52	thing you do is you always write down what we
01:54	have been given six m and you try to find
01:58	a conversion factor that will go directly from meters two
02:01	millimeters . Now in this case we have one ,
02:02	we have we know that millie means 1000 times smaller
02:06	, so we know that there are 1000 of these
02:08	small millimeters that fit inside of a meter . We
02:11	could use that in the conversion structure here . And
02:14	it would give us the correct answer . But let's
02:16	go a different way . Let's go a different path
02:18	, let's go from meters two centimeters . And then
02:21	from centimeters two millimeters . Let's use two conversion factors
02:24	just to get some practice . So we know that
02:27	in one of these meters we must have 100 of
02:30	these smaller centimeters because a centimeter is 100 times smaller
02:35	than a meter . So the meters cancel in this
02:38	case , the meters divide away with the meters and
02:40	if we stop the calculation here , we're going to
02:43	be left with centimeters but we don't want to stop
02:46	here . We want to go from centimeters two millimeters
02:49	, one centimeter is 10 millimeters , so one centimeter
02:52	is 10 millimeters . Yes , right . And we
02:57	arrange it this way instead of upside down , because
02:59	this is the only way the centimeters will cancel with
03:01	the centimeters . So all of my units have cancelled
03:03	the meters divided with the meters to give me one
03:06	. So they divide away the centimeters divided with the
03:08	centimeters that gave me one . So they all cancelled
03:11	. The only unit I have left is millimeters .
03:14	So now we have to multiply what is six times
03:17	100 right ? Six times 100 and 600 . Right
03:20	? So let's say that six times 100 and 600
03:23	. And then we still have to multiply by 10
03:26	. What is 600 times 10 ? Right ? Well
03:29	zero times 000 times 000 time six . Again ,
03:32	zero dropped 01 times zero is 01 times zero is
03:38	01 time 6 to 6 . We add these together
03:41	, we're going to get 6000 . So six times
03:44	100 , times 10 more is 6000 . And the
03:48	unit we have leftover is millimeters . So what we
03:51	have figured out is that in six m there should
03:55	be 6000 of these little tiny millimeters in there .
03:58	Let's see if it makes sense . We know that
04:01	in one m we have 1000 of these millimeters .
04:04	So if we have six times the length , we
04:06	should have six times the millimeters , which is what
04:08	we get there . Now we , I use to
04:11	conversion factors because I wanted to give you practice ,
04:14	but if you wanted to you could set the calculation
04:16	up a different way . If you wanted to ,
04:19	you could say six m And we could go directly
04:22	. one m is equal to 1000 , mm ,
04:26	m 1000 . Look what's going to happen . The
04:31	meters will cancel with the meters and you'll have six
04:33	times 1000 which will be 6000 millimeters . So the
04:38	point of the story here is not to make you
04:40	waste your time doing extra work is I want you
04:42	to know that no matter how you use your conversion
04:45	factors if you're using them correctly . If you're mapping
04:48	a path from point A to point B through the
04:51	correct conversion factors , no matter which factors you go
04:54	through , you will get the correct answer . You
04:56	will get to the single correct answer . No matter
04:58	which ones you use . All right , I won't
05:02	do the other ones multiple ways , but just wanted
05:04	to do that one . Let's take a look at
05:05	a large number 900,000 cm and we want to convert
05:11	that to km . So the first thing we do
05:15	is we write down what we are given 900,000 centimeters
05:20	and we need to try to go two kilometers .
05:23	But the problem is I don't have a conversion factor
05:26	that goes directly from centimeters two kilometers . I don't
05:28	have one , so I can't use that . But
05:30	what I can do is I can start with centimeters
05:32	and I can go two m and then once I
05:34	met meters , I'm over here and then I can
05:36	go two kilometers . So I can use this conversion
05:39	factor and then use this conversion factor 100 centimeters for
05:43	every one m , 100 centimeters for every one m
05:48	. Alright , I arrange it like that so that
05:51	the centimeters will cancel . If I stop the calculation
05:54	here , I'm going to be at meters . Now
05:56	, I have to go say one kilometer , 1000
05:59	m . So 1000 meters , one kg metre .
06:06	Why do I arrange it like this instead of flipping
06:09	it over ? Because this way the meters cancel with
06:11	the meters . So now the unit I have left
06:14	is kilo meters . All right . So now what
06:17	I have to do Is figure out a way to
06:19	multiply this . Now if you have a calculator ,
06:21	you'll just take 900 times one divided by 100 times
06:25	one divided by 1000 . Um but we don't we're
06:28	not using a calculator here . So I'm gonna show
06:30	you how I would I would really do it on
06:32	the top . You have 900,000 times one times one
06:35	. You have 900 1000 times one times one means
06:39	you have still have 900,000 on the bottom . You're
06:42	going to have 100 times 1000 . What is 100
06:45	times 1000 ? What is 1000 times 100 ? You
06:51	can multiply that by saying zero times 00 zero times
06:55	00000000 , dropped 00 times 000 times 000000 times 00
07:04	Okay now I have to drop to 01 times 001
07:08	times 001 times 00 and one times one . Finally
07:11	is a one . And I add all this stuff
07:13	up . I'm gonna have 100000 That's what I'm gonna
07:17	have . 100,100 1000 900,000 on the top , 100,000
07:24	on the bottom . But I see right away that
07:27	I have a ton of zeros . I don't want
07:28	to do this long division . I want to cancel
07:29	zeroes , zero cancels with this 10 cancels with 00
07:33	cancels with 00 cancels with 00 cancels with zero .
07:37	All I really have left is nine divided by one
07:41	Which is what nine divided by one is 9 .
07:45	And the unit is km . So the answer is
07:48	that I get is nine kilometers . Again , if
07:50	you have a calculator you can just divide it and
07:52	be done . But the way that I like to
07:54	do it without a calculator is multiply the tops ,
07:57	multiply the bottoms . You're gonna have tons of zeros
07:59	that you can then cancel . And then um you
08:03	know from there you cancel those zeros . And the
08:05	division becomes very , very simple Because I don't want
08:07	to go on a sheet of paper and divide 900,000
08:10	divided by 100,000 . So the next problem , 25,000
08:16	millimeters . Let's convert that two m . So we
08:21	write down what we are given 25,000 millimeters and we're
08:28	going to be converting that to uh , meters .
08:32	So millimeters to meters . That's what we want ,
08:34	millimeters to meters . Now we know in this one
08:37	again the same kind of thing . I wrote down
08:39	that 1 1000 millimeters fit in a meter that's totally
08:42	fine . We could use that conversion factor . But
08:44	to get a little more practice , let's do it
08:46	differently . Let's go from millimeters to centimeters . And
08:50	then from centimeters to meters just to get practiced with
08:53	using a different conversion factor . So one centimeter into
08:56	10 millimeters 10 millimeters for every one centimeter . And
09:02	I arrange it like this because here millimeters cancel with
09:05	millimeters . Now , if I stop the calculation here
09:07	, I'm gonna have centimeters . So I go over
09:09	here and say centimeters to meters . 100 centimeters fit
09:13	in a meter . So 100 centimeters fit in one
09:19	m . And I arrange it like this so that
09:22	centimeters cancels with centimeters . All right . So now
09:25	what do I have ? 25,000 times one times one
09:29	. So I'm gonna have 25,000 on the top .
09:33	And what am I going to have on the bottom
09:35	? What's 10 times 100 ? Right . You can
09:37	do the long form on the end here , but
09:40	when you think about 100 times 10 just cover up
09:42	the zero . What's 100 times one ? 100 times
09:45	100 . And I just add a zero and end
09:48	. It's going to be 1000 . So I just
09:50	take this times one is 100 then add one more
09:54	zero is going to be 1000 . If you don't
09:55	like that , just take 100 times 10 and do
09:58	the multiplication zero multiply zero . Multiply zero dropped zero
10:03	. Multiply here . Get zero multiple hair . Get
10:05	zero multiply here . Get a one and you can
10:07	see that it's 1000 . So I have 25,000 on
10:10	the top and 1000 on the bottom . Now I
10:13	can do this division where I can start canceling zeros
10:16	that cancels with that , that cancels that , that
10:18	cancels with that . And it just makes it much
10:20	easier because now all I have Is 25 divided by
10:23	one , which is 25 and the unit here is
10:26	meters . So the answer to all of that mess
10:28	was 25 m , 25,000 . It's 25 m .
10:34	Now I did a two step conversion process so you
10:37	get some practice with it . I could do a
10:38	conversion using only one step because I gave it to
10:41	you . But I'm trying to show you different ways
10:43	of doing things so that you can get the hang
10:45	of what happens if I have to use two conversions
10:48	, I don't want you to be scared of that
10:49	. So that's why we're doing it . Yeah .
10:52	All right , let's take a look at two km
10:55	, 2 km and let's convert it to cm .
10:58	So we write down what we are given two km
11:02	. How can I go from kilometers directly ? The
11:04	centimeters Actually , I don't have a way to go
11:07	directly from kilometers two centimeters , but I can go
11:10	from kilometers two m and then I can go from
11:13	meters two centimeters . So I have to do two
11:15	steps , one kilometer , 1000 m , right ?
11:20	One kilometer 1000 m . So I have one kilometer
11:24	1000 m . If I stop here with the cancellation
11:30	here , I'm going to end up with the unit
11:31	of meters . Now , how do I go from
11:33	meters two centimeters ? I know from the chart over
11:37	there . Plus just knowing what it means , is
11:40	that for every one m I have , I'm gonna
11:41	have 100 of these small centimeters in there and then
11:47	meters canceled with meters . So again , everything cancels
11:49	. Now , I have centimeters as my answer .
11:52	So what do I have to do ? Two times
11:55	1000 times 100 . Right , so what do I
11:58	do here ? Two times 1000 ? What do you
12:00	think that's going to be ? Well , you cover
12:01	up the zeros , you're gonna get to two times
12:04	one is to add the zeros back in . You're
12:06	gonna have uh 2000 . So 2000 is what two
12:11	times 1000 is . And I still have to multiply
12:14	this times 100 . But you see it's the same
12:17	thing . I know it's gonna be 2000 times this
12:20	, so I can cover up the zeros 2000 times
12:23	one is 2000 . And then I can add the
12:27	zeros back in the end . And that's gonna be
12:30	what I get now . If you don't like that
12:31	, we can multiply it out zero times 000 times
12:34	000000 attempts to zero dropped 00 times 200 times 000
12:41	times 000 times two . Again , zero dropped to
12:44	01 times 001 times 001 times 001 times two is
12:49	two . And you see when you add all this
12:50	together , you're going to get 200,000 this pen is
12:54	is not so great , but 400,000 . So two
12:59	times this is gonna be too . And then you
13:02	add the zero , so 2000 2000 times this is
13:05	gonna be 2000 with two more zeros at the end
13:08	. The ones on the bottom aren't gonna matter .
13:10	And so the answer that you get is 200,000 centimeters
13:14	200,000 senator . Big number . But that's the way
13:18	it goes from here on out . When we do
13:21	the problems , if we have to multiply large thing
13:24	, I'm not going to do that anymore . I'm
13:26	not gonna do this long form . You know how
13:28	to multiply things ? You can certainly multiply it yourself
13:31	. I'm showing you the way because of the zeroes
13:33	, it makes it so much easier to ignore the
13:35	zeros and then just tack them on to the end
13:38	. So that would be the last time that we
13:39	do a really long thing like this . Let's take
13:42	a look at the next problem . 11 m .
13:44	Let's convert it into mm . So we write down
13:49	what we are given 11 m now , how do
13:52	I go ? Two millimeters ? Of course . I
13:54	know how many millimeters fit in a meter , right
13:57	? I can say 1000 millimeters . one m .
14:01	There's no problem with that . But let's go a
14:02	different way just to get practice . one m is
14:05	a 100 centimeters So I can go meters , two
14:08	centimeters and then centimeters to meters . So one m
14:11	100 centimeters one m 100 cm . Right ? So
14:18	the meters cancel . If I stop the calculation ,
14:21	I'll be left with centimeters . So let's not stop
14:24	. Let's keep going . We know that one centimeter
14:26	is 10 millimeters . All right . And so then
14:32	the cm cancel . So now what do I have
14:35	left ? I have 11 times 100 divide by one
14:39	times 10 , divide by one . The ones aren't
14:41	gonna do anything . So 11 times uh 11 times
14:48	100 is going to be 11 times one is 11
14:53	and then two zeros at the end . So 11
14:55	times the 100 give you 1100 . Now , let's
14:58	take that 1100 . And let's multiply by the 10
15:02	same thing , ignore the 0 , 1100 times one
15:05	is 1100 Add one more 0 And you get to
15:09	11,000 . So the answer is 11,000 millimeters . Now
15:16	, if you want to multiply those in a long
15:18	way and add the zeros and add it all up
15:20	, I mean that's fine , but I'm trying to
15:21	tell you that basically when you multiply by things that
15:24	have zeros , you just ignore the zeros and then
15:27	you put the zeros at the end . So it's
15:29	11,000 . All right , let's move along . Let's
15:35	take a look at 600,000 Centim . Let's convert that
15:40	two km , 600,000 cm . Let's go two km
15:45	. So let's start with 600,000 centimetres And we need
15:50	a conversion that goes from centimeters directly the kilometers ,
15:53	but we don't have one . We don't have a
15:56	conversion directly from centimeters two kilometers . But I can
15:59	go from 100 centimeters that go in a meter and
16:02	then I can go from meters two kilometers . I
16:04	have to use a two step conversion . So what
16:07	am I going to do ? I'm going to say
16:10	that there are 100 of these little centimeters in every
16:13	one m and I arrange it like that so that
16:16	the centimeters will cancel with the centimeters and then I
16:20	say because I'm going to kilometers , I'll say that
16:23	there are 1000 of these meters in the really large
16:27	unit called a kilometer meters canceled with meters . So
16:32	you see now what I have to do is 600,000
16:34	on the top and then I have this stuff on
16:36	the bottom . So let's see if we can figure
16:37	out what we need to do . I'm going to
16:39	have 600 1000 on the top . What am I
16:43	going to actually have on the bottom ? 100 times
16:46	1000 . So let's just cover this up . What's
16:49	100 times one ? That's 100 . Right , So
16:52	we have 100 so 100 times 100 but we have
16:56	to add all the zeros in . So let me
16:57	add three more zeros And you have 100,000 on the
17:01	bottom . So again , you can do the long
17:02	form multiplication . There's nothing wrong with that . You're
17:04	going to get 100,000 . Now . Instead of doing
17:07	this division , I'll strike zero with zero , this
17:10	zero with this zero this zero with this hero .
17:12	Keep going , keep going , keep going , keep
17:14	going . All I have at the end of it
17:16	is six divided by one . You know how to
17:18	divide . six divided by one . It's just six
17:21	and the unit is km . And so what we
17:25	figured out is that 600,000 cm is six km .
17:29	And I'm not gonna lie . You have big numbers
17:31	here , but notice that we don't really need to
17:33	do this long for multiplication . I mean , you
17:35	kind of need it as a crutch in the beginning
17:37	, but once you learn how to multiply by and
17:39	divide by powers of 10 than it actually becomes easier
17:43	. All right , only a couple more problems .
17:45	Let's take a look at 16 1000 millimeters . And
17:51	we're going to convert that two m . All right
17:55	. So the first step is to write down 16,000
17:59	millimeters And we need to find a conversion factor that
18:02	goes directly to meters . Now we've done it straight
18:05	away several times with two steps . So this time
18:09	we're going to use the one that we know that
18:10	1000 of these tiny little mm fit in a meter
18:13	. We could use a two step conversion , but
18:15	let's just go ahead and use the one step this
18:17	one time . So 1000 of these tiny little millimeters
18:21	. Remember millimeter means 1000 times smaller than a meter
18:24	. So there has to be 1000 of these tiny
18:25	little things that fit in one m and millimeters cancels
18:31	with millimeters . So what do I have ? I
18:33	have 16,000 on the top and I have 1000 On
18:39	the bottom . Now you can divide that if you
18:41	want . There's no problem with that , but it's
18:43	going to be easier to cancel , cancel , cancel
18:45	, cancel , cancel , cancel . So really all
18:47	you have is you have 16 divided by one ,
18:50	which is just 16 . And the unit is meters
18:54	. So the unit came out to 16 m and
18:57	you can see once we've done this many times we
18:58	can speed up a little bit . Let's take a
19:01	look at 17 km and let's turn it into centimeters
19:08	. Write down what we are given 17 km .
19:12	How do we go from km two cm ? How
19:16	do we go from kilometers two centimeters . We know
19:18	that we can go one kilometer to 1000 m .
19:21	Then we can go one m to 100 of these
19:23	smaller things called centimeters . So we have to use
19:26	a two step conversion . So we know that one
19:31	km is 1000 meters And then we can go from
19:37	one m to 100 of these smaller centimeters . Now
19:41	, why did I range it like this instead of
19:42	flipping them all over ? Because here the kilometers canceled
19:45	with kilometers and the meters canceled with the meter .
19:47	So I have my centimeters in the answer Now ,
19:50	what do I do 17 times this , times this
19:53	. So there's a couple different ways you can think
19:56	about it . I'm gonna go over here to the
19:58	bottom , I'm gonna say 1000 times the 100 .
20:02	What is 1000 times the 100 ? Well , just
20:05	cover up the zeros . What's 1000 times one ?
20:07	Just 1000 And then the 100 to 2 zeros that
20:11	I covered up . Just go to the end .
20:12	So these to multiply to give me this . So
20:15	, what is 17 times this ? Well , I'll
20:17	cover up this one and it's gonna be 17 with
20:20	all of these zeros at the end . So I
20:22	have 12345 zeros at the end . Uh here ,
20:27	which is one point or 1,700,000 cm . Because cm
20:34	is the only unit left . So you could do
20:36	this times this and then take that times this .
20:38	That's 17,000 times this . You're gonna get the same
20:40	thing . I just choose to multiply these first .
20:42	It's easy to get this and then take this multiply
20:45	it by this . You're dividing by one also .
20:47	But that doesn't do anything . All right , now
20:50	, we're at our last problem Actually . Almost our
20:54	last problem . Take a look at eight m .
20:56	Let's convert that into mm . So we start off
20:59	with eight m again , I'm gonna allow us to
21:02	use our metric conversion instead of doing the two step
21:05	. We know that one m has to have 1000
21:08	of these tiny little millimeters because millie means 1000 times
21:12	smaller , so it has to be 1000 of them
21:14	fit in there . Meters will cancel with meters .
21:17	And what do we get ? Eight times 1000 .
21:19	You cover up the one , you get eight times
21:21	one is eight . And then you put the zeros
21:23	at the end 8000 millimeters . That's the final answer
21:27	. You see how fast it goes . Once we
21:29	know what we're doing . And then we have our
21:32	final problem for our last bit of practice 300 1000
21:37	centimetres . Let's convert it to kilometers . So we
21:41	start with what we have 300 centimetres , How do
21:46	we go from centimeters two kilometers anyway ? Well ,
21:49	we know we can go to meters and then we
21:51	can go from meters two kilometers . So let's write
21:53	that down how many meters fit or how many centimeters
21:56	fit in a meter . There are 100 of these
21:58	smaller centimeters in one m centimetres , cancel . If
22:03	I stop here , I have meters now meters two
22:05	kilometers . There have to be 1000 of these meters
22:08	that fit in the large unit of a kilometer .
22:11	And those cancel . So now I have this leftover
22:15	. So what I'm going to have at the end
22:17	of it is I'm going to have 300 1000 on
22:21	the top times one times one . So that's all
22:23	it's there . And then on the bottom , I'm
22:25	gonna have 1000 with these two zeros at the end
22:28	. Because if I multiply these , I can cover
22:29	this up 1000 times one is 1000 and I'm gonna
22:33	add the zero . So you're going to have 1000
22:36	and then you're gonna have these two zeros tacked on
22:38	the end . All right now you can divide that
22:41	. But it's just way easier , cancel , cancel
22:44	, cancel , cancel , cancel , cancel , cancel
22:46	, cancel , cancel , cancel . All you have
22:48	is three divided by one , which is now three
22:51	and the unit is kilometers . So we have found
22:56	out that 300,000 cm is three km . So we
23:00	were able to speed up in the end a little
23:03	bit because I'm showing you lots of things at once
23:05	. I'm showing you how to convert the units .
23:07	I'm showing you what the units mean . I'm showing
23:09	you how to set the conversion up . And I'm
23:11	also showing you how to multiply and divide by large
23:13	powers of 10 . Really easily . look at one
23:16	of the pain . This is to multiply all these
23:18	zeros and add them all up . You don't have
23:20	to do that . If you're multiplying times 100 just
23:22	cover it up . 1000 times the one right ?
23:25	Get 1000 , add the Zeros at the end ,
23:28	you get the 1000 with the two zeros here at
23:30	it at the end and we've been doing that over
23:32	and over . If you're dividing , then you're canceling
23:34	and striking through Zeros to make your problem easier .
23:37	And that is a really important lesson also above and
23:39	beyond the conversion here . So we're done with metric
23:42	system unit of length . We're going to work on
23:44	area and perimeter next . And then we're gonna go
23:47	back into the metric system , we're gonna talk about
23:49	metric units of volume and metric units of mass .
23:52	And so I'd like you to make sure you understand
23:54	this . Follow me on to the next lesson will
23:55	continue building your skills

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Learn Metric System & Unit Conversions - Dimensional Analysis - Math, Physics, Chemistry - [16] is a free educational video by Math and Science.

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