1
00:00:00,880 --> 00:00:03,310
Welcome to the
presentation on units.

2
00:00:03,310 --> 00:00:05,390
Let's get started.

3
00:00:05,390 --> 00:00:12,770
So if I were to ask you, or if
I were to say, I have traveled

4
00:00:12,770 --> 00:00:20,910
0.05 kilometers-- some
people say KIL-ometers

5
00:00:20,910 --> 00:00:22,020
or kil-O-meters.

6
00:00:22,020 --> 00:00:23,435


7
00:00:23,435 --> 00:00:24,850
If I have traveled 0.05
kilometers, how many

8
00:00:28,250 --> 00:00:30,865
centimeters have I traveled?

9
00:00:30,865 --> 00:00:32,590
That's question
mark centimeters.

10
00:00:32,590 --> 00:00:35,880
So before we break into the
math, it's important to just

11
00:00:38,390 --> 00:00:41,730
know what these prefixes
centi and kilo mean.

12
00:00:41,730 --> 00:00:44,650
And it's good to memorize this,
or when you're first starting

13
00:00:44,650 --> 00:00:46,130
to do these problems, you can
just write them down on a piece

14
00:00:46,130 --> 00:00:48,080
of paper, just so you
have a reference.

15
00:00:48,080 --> 00:01:06,460
So kilo means 1,000, hecto
means 100, deca means 10.

16
00:01:06,460 --> 00:01:09,840
You might recognize that
from decade, 10 years.

17
00:01:09,840 --> 00:01:13,980
And then, of course, you
have no prefix, means 1.

18
00:01:13,980 --> 00:01:15,580
No prefix.

19
00:01:15,580 --> 00:01:18,710
No prefix equals 1.

20
00:01:18,710 --> 00:01:28,100
deci is equal to 0.1 or 1/10.

21
00:01:28,100 --> 00:01:32,510
centi-- I keep changing
between cases.

22
00:01:32,510 --> 00:01:38,590
centi is equal to
0.01, or 1/100.

23
00:01:38,590 --> 00:01:45,110
And then milli is equal
to 0.001, and that's the

24
00:01:45,110 --> 00:01:48,710
same thing as 1/1,000.

25
00:01:48,710 --> 00:01:52,810
And the way I remember, I mean,
centi, if you think of a

26
00:01:52,810 --> 00:01:54,740
centipede, it has a 100 feet.

27
00:01:54,740 --> 00:01:58,360
A millipede, I'm not sure if a
millipede has 1,000 feet, but

28
00:01:58,360 --> 00:02:00,850
that's the implication when
someone says a millipede

29
00:02:00,850 --> 00:02:02,550
because pede means feet.

30
00:02:02,550 --> 00:02:03,810
So let's go back
to the problem.

31
00:02:03,810 --> 00:02:08,490
If I have 0.05 kilometers, how
many centimeters do I have?

32
00:02:08,490 --> 00:02:10,350
Whenever I do a problem like
this, I like to actually

33
00:02:10,350 --> 00:02:12,930
convert my number to
meters because that's

34
00:02:12,930 --> 00:02:14,290
very easy for me.

35
00:02:14,290 --> 00:02:18,150
And actually, I'm going to
abbreviate this is km, and

36
00:02:18,150 --> 00:02:21,530
we can abbreviate this
as cm for centimeters.

37
00:02:21,530 --> 00:02:28,480
So let's say 0.05 km.

38
00:02:28,480 --> 00:02:32,500
Well, if I want to convert this
into meters, is it going to be

39
00:02:32,500 --> 00:02:37,150
more than 0.05 meters
or less than 0.05?

40
00:02:37,150 --> 00:02:40,820
Well, a kilometer is a very
large distance, so in terms

41
00:02:40,820 --> 00:02:43,430
of meters, it's going to
be a much bigger number.

42
00:02:43,430 --> 00:02:52,600
So we can multiply this times
1,000 meters, and I'll do

43
00:02:52,600 --> 00:02:53,880
it over 1, per kilometer.

44
00:02:53,880 --> 00:02:56,490
And what does that get?

45
00:02:58,050 --> 00:03:04,890
Well, 0.05 times 1,000
is equal to 50, right?

46
00:03:04,890 --> 00:03:07,670
I just multiplied
0.05 times 1,000.

47
00:03:07,670 --> 00:03:12,610
And with the units, I now
have kilometers times

48
00:03:12,610 --> 00:03:16,260
meters over kilometers.

49
00:03:16,260 --> 00:03:18,290
And the kilometers cancel out.

50
00:03:18,290 --> 00:03:22,260
And just so you're familiar
with this, you can treat units

51
00:03:22,260 --> 00:03:24,640
exactly the same way that you
would treat numbers

52
00:03:24,640 --> 00:03:25,670
or variables.

53
00:03:25,670 --> 00:03:28,990
As long as you have the same
unit in the numerator and the

54
00:03:28,990 --> 00:03:30,970
denominator, you can cancel
them out, assuming that you're

55
00:03:30,970 --> 00:03:33,490
not adding units, you're
multiplying units.

56
00:03:33,490 --> 00:03:36,540
So you have kilometers times
meters divided by kilometers,

57
00:03:36,540 --> 00:03:40,030
and that equals 50 meters.

58
00:03:40,030 --> 00:03:43,890
And it's good to always do a
reality check after every step.

59
00:03:43,890 --> 00:03:45,700
Usually when you do these types
of problems, you know, OK, if I

60
00:03:45,700 --> 00:03:48,780
want to go from kilometers to
meters, I'm going to use the

61
00:03:48,780 --> 00:03:51,010
number 1,000, because that's
the relationship between

62
00:03:51,010 --> 00:03:52,170
a kilometer and a meter.

63
00:03:52,170 --> 00:03:54,830
And you're always confused,
well, do I multiply by 1,000,

64
00:03:54,830 --> 00:03:56,250
or do I divide by 1,000?

65
00:03:56,250 --> 00:03:58,720
And you always have to say,
well, if I'm going from

66
00:03:58,720 --> 00:04:03,050
kilometers to meters, I'm
going-- 1 kilometer is

67
00:04:03,050 --> 00:04:05,550
1,000 meters, right?

68
00:04:05,550 --> 00:04:07,820
So I'm going to be
multiplying by 1,000.

69
00:04:07,820 --> 00:04:09,130
I'm going to get
a bigger number.

70
00:04:09,130 --> 00:04:12,490
So that's why I went from
0.05, and I multiplied it

71
00:04:12,490 --> 00:04:14,600
by 1,000, and I got 50.

72
00:04:14,600 --> 00:04:16,100
So let's get back
to the problem.

73
00:04:16,100 --> 00:04:19,400
0.05 kilometers is
equal to 50 meters.

74
00:04:19,400 --> 00:04:20,210
We're not done yet.

75
00:04:20,210 --> 00:04:23,280
Now, you need to convert those
50 meters into centimeters.

76
00:04:23,280 --> 00:04:25,540
Well, we do the same thing.

77
00:04:25,540 --> 00:04:32,730
50 meters times-- how many-- so
what's the relationship between

78
00:04:32,730 --> 00:04:33,740
meters and centimeters?

79
00:04:33,740 --> 00:04:36,320
Well, if we look at the
chart, we see it's 100.

80
00:04:36,320 --> 00:04:38,310
And the question I'm going to
ask you, am I going to multiply

81
00:04:38,310 --> 00:04:41,580
by 100, or am I going
to divide by 100?

82
00:04:41,580 --> 00:04:42,520
Well, it's the same thing.

83
00:04:42,520 --> 00:04:45,320
We're going from a bigger unit
to a smaller unit, so one of

84
00:04:45,320 --> 00:04:48,240
a bigger unit is equal to a
bunch of the smaller units.

85
00:04:48,240 --> 00:04:50,330
So we're going to multiply.

86
00:04:50,330 --> 00:04:56,590
So we say times 100
centimeters per meter, right?

87
00:04:56,590 --> 00:04:57,330
And that just makes sense.

88
00:04:57,330 --> 00:04:59,710
There's 100 centimeters
per meter.

89
00:04:59,710 --> 00:05:02,840
So 50 meters times 100
centimeters per meter is equal

90
00:05:02,840 --> 00:05:12,625
to 50 times 100 is 5,000, and
then the meters cancel out,

91
00:05:12,625 --> 00:05:15,260
and you get centimeters.

92
00:05:15,260 --> 00:05:21,330
So what we have here is that
0.05 kilometers is equal

93
00:05:21,330 --> 00:05:24,850
to 5,000 centimeters.

94
00:05:24,850 --> 00:05:26,090
Let's do another problem.

95
00:05:26,090 --> 00:05:28,580
I think the more examples
you see, it'll make them

96
00:05:28,580 --> 00:05:28,940
a little more sense.

97
00:05:28,940 --> 00:05:31,360
And always try to visualize
what we're doing, the scale.

98
00:05:31,360 --> 00:05:32,830
Otherwise, it's very
confusing whether you

99
00:05:32,830 --> 00:05:36,020
should multiply or divide.

100
00:05:36,020 --> 00:05:41,100
Let's say I have 422 decigrams.

101
00:05:41,100 --> 00:05:47,110
Grams are a measure of mass.

102
00:05:49,530 --> 00:05:51,470
One gram is actually
a very small amount.

103
00:05:51,470 --> 00:05:53,710
That's what you measure--
I guess in the metric

104
00:05:53,710 --> 00:05:56,770
system, they measure
gold in terms of grams.

105
00:05:56,770 --> 00:06:03,180
And I want to convert
this into milligrams.

106
00:06:03,180 --> 00:06:07,200
So before we start the problem,
let's just do a reality check.

107
00:06:07,200 --> 00:06:09,700
Am I going from a bigger unit
to a smaller unit, or a smaller

108
00:06:09,700 --> 00:06:10,870
unit to a bigger unit?

109
00:06:10,870 --> 00:06:18,870
Well, decigrams, that's 1/10
of a gram, and I'm going

110
00:06:18,870 --> 00:06:23,110
to 1/1,000 of a gram.

111
00:06:23,110 --> 00:06:25,750

So there's two ways
of doing this.

112
00:06:26,960 --> 00:06:29,940
We can convert to grams and
then convert to the other unit.

113
00:06:29,940 --> 00:06:32,350
That sometimes
make things easy.

114
00:06:32,350 --> 00:06:35,910
Or we could say, well,
how many milligrams is

115
00:06:35,910 --> 00:06:37,920
equal to one decigram?

116
00:06:37,920 --> 00:06:42,140
Well, a milligram, as
we see here, is 100

117
00:06:42,140 --> 00:06:43,270
times smaller, right?

118
00:06:43,270 --> 00:06:47,330
To go from 1/10 to 1/1,000,
you have to decrease

119
00:06:47,330 --> 00:06:48,780
in size by 100.

120
00:06:48,780 --> 00:07:02,570
So we could just say 422
decigrams times 100

121
00:07:02,570 --> 00:07:08,230
milligrams per decigram.

122
00:07:08,230 --> 00:07:12,390

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

123
00:07:17,620 --> 00:07:24,405
times 100, 42,200 milligrams.

124
00:07:24,405 --> 00:07:29,950

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

125
00:07:31,790 --> 00:07:32,810
did that last problem.

126
00:07:32,810 --> 00:07:36,880
We could say 422 decigrams, we
could convert that to grams.

127
00:07:36,880 --> 00:07:41,620
We could say 422-- I'm
just going to say dg.

128
00:07:41,620 --> 00:07:45,500
That's not really a
familiar unit-- decigrams.

129
00:07:45,500 --> 00:07:48,150
And how many decigrams
are there per gram?

130
00:07:48,150 --> 00:07:51,260
If we're going to gram, 422
is going to be a smaller

131
00:07:51,260 --> 00:07:53,360
number of grams, right?

132
00:07:53,360 --> 00:07:59,110
So we could say times
1 decigram is equal

133
00:07:59,110 --> 00:08:01,230
to how many grams?

134
00:08:01,230 --> 00:08:07,200
Well, 1 decigram is
equal to-- no, sorry.

135
00:08:07,200 --> 00:08:09,800
1 gram is equal to
how many decigrams?

136
00:08:09,800 --> 00:08:13,650
Well, 1 gram is equal
to 10 decigrams.

137
00:08:13,650 --> 00:08:16,560
And the reason why this makes
sense is if we have a decigram

138
00:08:16,560 --> 00:08:18,290
in the numerator here, we want
a decigram in the

139
00:08:18,290 --> 00:08:19,790
denominator here.

140
00:08:19,790 --> 00:08:26,480
So if we have decigrams cancel
out, 422 decigrams will equal--

141
00:08:26,480 --> 00:08:33,240
that divided by 10 is
equal to 42.2 grams.

142
00:08:33,240 --> 00:08:35,770
And now we can just go
from grams to milligrams.

143
00:08:35,770 --> 00:08:37,120
Well, that's an easy one.

144
00:08:37,120 --> 00:08:41,150
1 gram is equal to 1,000
milligrams, so we could say

145
00:08:41,150 --> 00:08:48,620
times 1,000 milligram per gram.

146
00:08:48,620 --> 00:08:53,680
The grams cancel out, and
we're left with 42,200

147
00:08:53,680 --> 00:08:55,310
milligrams, right?

148
00:08:55,310 --> 00:08:59,380
42.2 times 1,000.

149
00:08:59,380 --> 00:09:01,530
Hopefully, that doesn't
confuse you too much.

150
00:09:01,530 --> 00:09:04,330
The important thing is to
always take a step back and

151
00:09:04,330 --> 00:09:06,960
really visualize and think
about, should I be getting a

152
00:09:06,960 --> 00:09:09,310
larger number or a smaller
number than the one

153
00:09:09,310 --> 00:09:10,920
I started off with?

154
00:09:10,920 --> 00:09:13,840
I think you're ready to
now try some problems.

155
00:09:13,840 --> 00:09:15,320
Have fun!