WEBVTT

00:00:00.880 --> 00:00:03.310
Welcome to the
presentation on units.

00:00:03.310 --> 00:00:05.390
Let's get started.

00:00:05.390 --> 00:00:12.770
So if I were to ask you, or if
I were to say, I have traveled

00:00:12.770 --> 00:00:20.910
0.05 kilometers-- some
people say KIL-ometers

00:00:20.910 --> 00:00:22.020
or kil-O-meters.

00:00:22.020 --> 00:00:23.435


00:00:23.435 --> 00:00:24.850
If I have traveled 0.05
kilometers, how many

00:00:28.250 --> 00:00:30.865
centimeters have I traveled?

00:00:30.865 --> 00:00:32.590
That's question
mark centimeters.

00:00:32.590 --> 00:00:35.880
So before we break into the
math, it's important to just

00:00:38.390 --> 00:00:41.730
know what these prefixes
centi and kilo mean.

00:00:41.730 --> 00:00:44.650
And it's good to memorize this,
or when you're first starting

00:00:44.650 --> 00:00:46.130
to do these problems, you can
just write them down on a piece

00:00:46.130 --> 00:00:48.080
of paper, just so you
have a reference.

00:00:48.080 --> 00:01:06.460
So kilo means 1,000, hecto
means 100, deca means 10.

00:01:06.460 --> 00:01:09.840
You might recognize that
from decade, 10 years.

00:01:09.840 --> 00:01:13.980
And then, of course, you
have no prefix, means 1.

00:01:13.980 --> 00:01:15.580
No prefix.

00:01:15.580 --> 00:01:18.710
No prefix equals 1.

00:01:18.710 --> 00:01:28.100
deci is equal to 0.1 or 1/10.

00:01:28.100 --> 00:01:32.510
centi-- I keep changing
between cases.

00:01:32.510 --> 00:01:38.590
centi is equal to
0.01, or 1/100.

00:01:38.590 --> 00:01:45.110
And then milli is equal
to 0.001, and that's the

00:01:45.110 --> 00:01:48.710
same thing as 1/1,000.

00:01:48.710 --> 00:01:52.810
And the way I remember, I mean,
centi, if you think of a

00:01:52.810 --> 00:01:54.740
centipede, it has a 100 feet.

00:01:54.740 --> 00:01:58.360
A millipede, I'm not sure if a
millipede has 1,000 feet, but

00:01:58.360 --> 00:02:00.850
that's the implication when
someone says a millipede

00:02:00.850 --> 00:02:02.550
because pede means feet.

00:02:02.550 --> 00:02:03.810
So let's go back
to the problem.

00:02:03.810 --> 00:02:08.490
If I have 0.05 kilometers, how
many centimeters do I have?

00:02:08.490 --> 00:02:10.350
Whenever I do a problem like
this, I like to actually

00:02:10.350 --> 00:02:12.930
convert my number to
meters because that's

00:02:12.930 --> 00:02:14.290
very easy for me.

00:02:14.290 --> 00:02:18.150
And actually, I'm going to
abbreviate this is km, and

00:02:18.150 --> 00:02:21.530
we can abbreviate this
as cm for centimeters.

00:02:21.530 --> 00:02:28.480
So let's say 0.05 km.

00:02:28.480 --> 00:02:32.500
Well, if I want to convert this
into meters, is it going to be

00:02:32.500 --> 00:02:37.150
more than 0.05 meters
or less than 0.05?

00:02:37.150 --> 00:02:40.820
Well, a kilometer is a very
large distance, so in terms

00:02:40.820 --> 00:02:43.430
of meters, it's going to
be a much bigger number.

00:02:43.430 --> 00:02:52.600
So we can multiply this times
1,000 meters, and I'll do

00:02:52.600 --> 00:02:53.880
it over 1, per kilometer.

00:02:53.880 --> 00:02:56.490
And what does that get?

00:02:58.050 --> 00:03:04.890
Well, 0.05 times 1,000
is equal to 50, right?

00:03:04.890 --> 00:03:07.670
I just multiplied
0.05 times 1,000.

00:03:07.670 --> 00:03:12.610
And with the units, I now
have kilometers times

00:03:12.610 --> 00:03:16.260
meters over kilometers.

00:03:16.260 --> 00:03:18.290
And the kilometers cancel out.

00:03:18.290 --> 00:03:22.260
And just so you're familiar
with this, you can treat units

00:03:22.260 --> 00:03:24.640
exactly the same way that you
would treat numbers

00:03:24.640 --> 00:03:25.670
or variables.

00:03:25.670 --> 00:03:28.990
As long as you have the same
unit in the numerator and the

00:03:28.990 --> 00:03:30.970
denominator, you can cancel
them out, assuming that you're

00:03:30.970 --> 00:03:33.490
not adding units, you're
multiplying units.

00:03:33.490 --> 00:03:36.540
So you have kilometers times
meters divided by kilometers,

00:03:36.540 --> 00:03:40.030
and that equals 50 meters.

00:03:40.030 --> 00:03:43.890
And it's good to always do a
reality check after every step.

00:03:43.890 --> 00:03:45.700
Usually when you do these types
of problems, you know, OK, if I

00:03:45.700 --> 00:03:48.780
want to go from kilometers to
meters, I'm going to use the

00:03:48.780 --> 00:03:51.010
number 1,000, because that's
the relationship between

00:03:51.010 --> 00:03:52.170
a kilometer and a meter.

00:03:52.170 --> 00:03:54.830
And you're always confused,
well, do I multiply by 1,000,

00:03:54.830 --> 00:03:56.250
or do I divide by 1,000?

00:03:56.250 --> 00:03:58.720
And you always have to say,
well, if I'm going from

00:03:58.720 --> 00:04:03.050
kilometers to meters, I'm
going-- 1 kilometer is

00:04:03.050 --> 00:04:05.550
1,000 meters, right?

00:04:05.550 --> 00:04:07.820
So I'm going to be
multiplying by 1,000.

00:04:07.820 --> 00:04:09.130
I'm going to get
a bigger number.

00:04:09.130 --> 00:04:12.490
So that's why I went from
0.05, and I multiplied it

00:04:12.490 --> 00:04:14.600
by 1,000, and I got 50.

00:04:14.600 --> 00:04:16.100
So let's get back
to the problem.

00:04:16.100 --> 00:04:19.400
0.05 kilometers is
equal to 50 meters.

00:04:19.400 --> 00:04:20.210
We're not done yet.

00:04:20.210 --> 00:04:23.280
Now, you need to convert those
50 meters into centimeters.

00:04:23.280 --> 00:04:25.540
Well, we do the same thing.

00:04:25.540 --> 00:04:32.730
50 meters times-- how many-- so
what's the relationship between

00:04:32.730 --> 00:04:33.740
meters and centimeters?

00:04:33.740 --> 00:04:36.320
Well, if we look at the
chart, we see it's 100.

00:04:36.320 --> 00:04:38.310
And the question I'm going to
ask you, am I going to multiply

00:04:38.310 --> 00:04:41.580
by 100, or am I going
to divide by 100?

00:04:41.580 --> 00:04:42.520
Well, it's the same thing.

00:04:42.520 --> 00:04:45.320
We're going from a bigger unit
to a smaller unit, so one of

00:04:45.320 --> 00:04:48.240
a bigger unit is equal to a
bunch of the smaller units.

00:04:48.240 --> 00:04:50.330
So we're going to multiply.

00:04:50.330 --> 00:04:56.590
So we say times 100
centimeters per meter, right?

00:04:56.590 --> 00:04:57.330
And that just makes sense.

00:04:57.330 --> 00:04:59.710
There's 100 centimeters
per meter.

00:04:59.710 --> 00:05:02.840
So 50 meters times 100
centimeters per meter is equal

00:05:02.840 --> 00:05:12.625
to 50 times 100 is 5,000, and
then the meters cancel out,

00:05:12.625 --> 00:05:15.260
and you get centimeters.

00:05:15.260 --> 00:05:21.330
So what we have here is that
0.05 kilometers is equal

00:05:21.330 --> 00:05:24.850
to 5,000 centimeters.

00:05:24.850 --> 00:05:26.090
Let's do another problem.

00:05:26.090 --> 00:05:28.580
I think the more examples
you see, it'll make them

00:05:28.580 --> 00:05:28.940
a little more sense.

00:05:28.940 --> 00:05:31.360
And always try to visualize
what we're doing, the scale.

00:05:31.360 --> 00:05:32.830
Otherwise, it's very
confusing whether you

00:05:32.830 --> 00:05:36.020
should multiply or divide.

00:05:36.020 --> 00:05:41.100
Let's say I have 422 decigrams.

00:05:41.100 --> 00:05:47.110
Grams are a measure of mass.

00:05:49.530 --> 00:05:51.470
One gram is actually
a very small amount.

00:05:51.470 --> 00:05:53.710
That's what you measure--
I guess in the metric

00:05:53.710 --> 00:05:56.770
system, they measure
gold in terms of grams.

00:05:56.770 --> 00:06:03.180
And I want to convert
this into milligrams.

00:06:03.180 --> 00:06:07.200
So before we start the problem,
let's just do a reality check.

00:06:07.200 --> 00:06:09.700
Am I going from a bigger unit
to a smaller unit, or a smaller

00:06:09.700 --> 00:06:10.870
unit to a bigger unit?

00:06:10.870 --> 00:06:18.870
Well, decigrams, that's 1/10
of a gram, and I'm going

00:06:18.870 --> 00:06:23.110
to 1/1,000 of a gram.

00:06:23.110 --> 00:06:25.750

So there's two ways
of doing this.

00:06:26.960 --> 00:06:29.940
We can convert to grams and
then convert to the other unit.

00:06:29.940 --> 00:06:32.350
That sometimes
make things easy.

00:06:32.350 --> 00:06:35.910
Or we could say, well,
how many milligrams is

00:06:35.910 --> 00:06:37.920
equal to one decigram?

00:06:37.920 --> 00:06:42.140
Well, a milligram, as
we see here, is 100

00:06:42.140 --> 00:06:43.270
times smaller, right?

00:06:43.270 --> 00:06:47.330
To go from 1/10 to 1/1,000,
you have to decrease

00:06:47.330 --> 00:06:48.780
in size by 100.

00:06:48.780 --> 00:07:02.570
So we could just say 422
decigrams times 100

00:07:02.570 --> 00:07:08.230
milligrams per decigram.

00:07:08.230 --> 00:07:12.390

And then the decigrams will
cancel out, and I'll get 422

00:07:17.620 --> 00:07:24.405
times 100, 42,200 milligrams.

00:07:24.405 --> 00:07:29.950

Now, another way you could have
done it is the way we just

00:07:31.790 --> 00:07:32.810
did that last problem.

00:07:32.810 --> 00:07:36.880
We could say 422 decigrams, we
could convert that to grams.

00:07:36.880 --> 00:07:41.620
We could say 422-- I'm
just going to say dg.

00:07:41.620 --> 00:07:45.500
That's not really a
familiar unit-- decigrams.

00:07:45.500 --> 00:07:48.150
And how many decigrams
are there per gram?

00:07:48.150 --> 00:07:51.260
If we're going to gram, 422
is going to be a smaller

00:07:51.260 --> 00:07:53.360
number of grams, right?

00:07:53.360 --> 00:07:59.110
So we could say times
1 decigram is equal

00:07:59.110 --> 00:08:01.230
to how many grams?

00:08:01.230 --> 00:08:07.200
Well, 1 decigram is
equal to-- no, sorry.

00:08:07.200 --> 00:08:09.800
1 gram is equal to
how many decigrams?

00:08:09.800 --> 00:08:13.650
Well, 1 gram is equal
to 10 decigrams.

00:08:13.650 --> 00:08:16.560
And the reason why this makes
sense is if we have a decigram

00:08:16.560 --> 00:08:18.290
in the numerator here, we want
a decigram in the

00:08:18.290 --> 00:08:19.790
denominator here.

00:08:19.790 --> 00:08:26.480
So if we have decigrams cancel
out, 422 decigrams will equal--

00:08:26.480 --> 00:08:33.240
that divided by 10 is
equal to 42.2 grams.

00:08:33.240 --> 00:08:35.770
And now we can just go
from grams to milligrams.

00:08:35.770 --> 00:08:37.120
Well, that's an easy one.

00:08:37.120 --> 00:08:41.150
1 gram is equal to 1,000
milligrams, so we could say

00:08:41.150 --> 00:08:48.620
times 1,000 milligram per gram.

00:08:48.620 --> 00:08:53.680
The grams cancel out, and
we're left with 42,200

00:08:53.680 --> 00:08:55.310
milligrams, right?

00:08:55.310 --> 00:08:59.380
42.2 times 1,000.

00:08:59.380 --> 00:09:01.530
Hopefully, that doesn't
confuse you too much.

00:09:01.530 --> 00:09:04.330
The important thing is to
always take a step back and

00:09:04.330 --> 00:09:06.960
really visualize and think
about, should I be getting a

00:09:06.960 --> 00:09:09.310
larger number or a smaller
number than the one

00:09:09.310 --> 00:09:10.920
I started off with?

00:09:10.920 --> 00:09:13.840
I think you're ready to
now try some problems.

00:09:13.840 --> 00:09:15.320
Have fun!