1
00:00:00,000 --> 00:00:00,500


2
00:00:00,500 --> 00:00:02,520
Throughout your
mathematical life,

3
00:00:02,520 --> 00:00:06,034
you will find situations where
you will need to round numbers.

4
00:00:06,034 --> 00:00:07,450
And you might be
saying, well why?

5
00:00:07,450 --> 00:00:09,090
What situations might that be?

6
00:00:09,090 --> 00:00:10,660
Well, these would
be situations where

7
00:00:10,660 --> 00:00:12,550
you're trying to get
an estimate on things.

8
00:00:12,550 --> 00:00:14,758
Where you're trying to--
maybe you have a measurement

9
00:00:14,758 --> 00:00:17,721
and you want it to be a little
bit less exact to simplify

10
00:00:17,721 --> 00:00:18,220
things.

11
00:00:18,220 --> 00:00:20,719
Or you don't trust how
exact the measurement is.

12
00:00:20,719 --> 00:00:23,260
So here we're going to actually
think about what rounding is.

13
00:00:23,260 --> 00:00:27,680
And we're going to round each of
these numbers, 36, 34, 35, 26,

14
00:00:27,680 --> 00:00:28,550
and 12.

15
00:00:28,550 --> 00:00:31,650
We're going to round each
of them to the nearest 10.

16
00:00:31,650 --> 00:00:33,750
And I'll give you a
hint of what that means.

17
00:00:33,750 --> 00:00:36,080
That essentially says take
each of these numbers,

18
00:00:36,080 --> 00:00:39,940
and find the multiple of
10 that it is closest to.

19
00:00:39,940 --> 00:00:41,300
So what are multiples of 10?

20
00:00:41,300 --> 00:00:43,750
Well, 10 times 0
is 0, 10 times 1

21
00:00:43,750 --> 00:00:48,695
is 10, 20, 30, 40, 50,
60, so on and so forth.

22
00:00:48,695 --> 00:00:50,320
So I encourage you
to pause this video,

23
00:00:50,320 --> 00:00:52,300
and just based on what I just
told you, what is the nearest

24
00:00:52,300 --> 00:00:54,130
multiple of 10 to
each of these numbers?

25
00:00:54,130 --> 00:00:56,297
Try to think about that.

26
00:00:56,297 --> 00:00:58,380
Well, to think about it a
little bit deeper, let's

27
00:00:58,380 --> 00:01:00,550
actually put a number line here.

28
00:01:00,550 --> 00:01:02,590
I'll put two number
lines over here.

29
00:01:02,590 --> 00:01:05,050
So we've got some
number lines here.

30
00:01:05,050 --> 00:01:06,940
And let's think about
where these points

31
00:01:06,940 --> 00:01:09,350
would sit on this number line.

32
00:01:09,350 --> 00:01:11,710
So this first number,
36, where does it

33
00:01:11,710 --> 00:01:13,410
sit on this number line?

34
00:01:13,410 --> 00:01:15,360
Well, it's between 30 and 40.

35
00:01:15,360 --> 00:01:18,180
And this little blue mark
is 35, it's halfway between.

36
00:01:18,180 --> 00:01:21,440
So 36 is going to be a
little higher than that.

37
00:01:21,440 --> 00:01:25,490
So 36 is going to
be right over here.

38
00:01:25,490 --> 00:01:28,430
And if we zoom in
between 30 and 40.

39
00:01:28,430 --> 00:01:33,170
So if we say that this
is 30, and this is 40,

40
00:01:33,170 --> 00:01:34,650
where is 36 going to be?

41
00:01:34,650 --> 00:01:36,110
So once again, this is 35.

42
00:01:36,110 --> 00:01:37,870
36 is one notch above that.

43
00:01:37,870 --> 00:01:41,700
So 36 is going to
be right over here.

44
00:01:41,700 --> 00:01:45,190
So if we want to round to the
nearest 10, to the nearest

45
00:01:45,190 --> 00:01:48,740
multiple of 10, what are
the two possibilities here?

46
00:01:48,740 --> 00:01:54,230
Well, I could take 36
and I could round up

47
00:01:54,230 --> 00:01:58,000
to the multiple of 10
above it, which is 40.

48
00:01:58,000 --> 00:02:02,100
So I could round up to
40, or I could round down

49
00:02:02,100 --> 00:02:08,160
to the multiple of 10
below it, which is 30.

50
00:02:08,160 --> 00:02:10,280
And so I need to figure
out which of these numbers

51
00:02:10,280 --> 00:02:11,600
is it closer to.

52
00:02:11,600 --> 00:02:14,335
Well, when you just look at
that, even just eyeballing it,

53
00:02:14,335 --> 00:02:14,960
you can see it.

54
00:02:14,960 --> 00:02:17,830
But you could also say 36
is only four away from 40,

55
00:02:17,830 --> 00:02:20,670
and it's six away from
30, it's closer to 40.

56
00:02:20,670 --> 00:02:22,820
So we are going to round up.

57
00:02:22,820 --> 00:02:25,240
We are going to round up to 40.

58
00:02:25,240 --> 00:02:27,460
This is literally
called rounding up.

59
00:02:27,460 --> 00:02:29,540
Now let's try some of
these other numbers.

60
00:02:29,540 --> 00:02:31,970
What about 34?

61
00:02:31,970 --> 00:02:34,126
And I encourage you
to pause the video.

62
00:02:34,126 --> 00:02:35,500
Think about what
number you would

63
00:02:35,500 --> 00:02:38,040
get if you were to try to
round it up or round it down,

64
00:02:38,040 --> 00:02:40,970
and then which one it
is actually closer to.

65
00:02:40,970 --> 00:02:46,950
Well, 34 is right over
here on this number line,

66
00:02:46,950 --> 00:02:52,220
where we zoom in, 34
is right over here.

67
00:02:52,220 --> 00:02:54,170
And we have two options.

68
00:02:54,170 --> 00:02:57,060
The multiple of
10 above 34-- let

69
00:02:57,060 --> 00:03:02,920
me do those same colors-- the
multiple of 10 above 34 is 40.

70
00:03:02,920 --> 00:03:06,809
Multiple of 10 below
34, again, is 30.

71
00:03:06,809 --> 00:03:08,100
Now, which one is it closer to?

72
00:03:08,100 --> 00:03:10,780
Well it's only four away from
30, and six away from 40,

73
00:03:10,780 --> 00:03:12,750
so it's closer to 30.

74
00:03:12,750 --> 00:03:15,700
So we are going to
round down to 30.

75
00:03:15,700 --> 00:03:19,750


76
00:03:19,750 --> 00:03:21,280
And notice we went to 30.

77
00:03:21,280 --> 00:03:22,863
You might say, hey,
when we rounded it

78
00:03:22,863 --> 00:03:26,280
up the 10's place increased
from 3 to 4, from 30 to 40.

79
00:03:26,280 --> 00:03:28,020
Maybe when we round
down, the 10's place

80
00:03:28,020 --> 00:03:30,970
will decrease from
30 to 20, but no, 30

81
00:03:30,970 --> 00:03:33,210
is the multiple of 10 below 34.

82
00:03:33,210 --> 00:03:35,460
So when you round
down, you just go--

83
00:03:35,460 --> 00:03:40,060
you keep the multiple of 10,
but the ones place becomes a 0.

84
00:03:40,060 --> 00:03:42,220
Now let's try a really
interesting one.

85
00:03:42,220 --> 00:03:48,165
Let's think about rounding the
number 35 to the nearest 10.

86
00:03:48,165 --> 00:03:49,790
And first, before we
even try to do it,

87
00:03:49,790 --> 00:03:51,090
let's think about
the two options.

88
00:03:51,090 --> 00:03:52,256
Well, we've already seen it.

89
00:03:52,256 --> 00:03:54,450
35 is sitting right over here.

90
00:03:54,450 --> 00:03:57,760
On this number line, that
is 35, and once again we

91
00:03:57,760 --> 00:03:59,200
have two options.

92
00:03:59,200 --> 00:04:07,270
35, we can round it up to 40,
or we could round it down to 30.

93
00:04:07,270 --> 00:04:10,430
And I encourage you to pause
the video and think about this.

94
00:04:10,430 --> 00:04:12,600
Well this one is a
little bit of a conundrum

95
00:04:12,600 --> 00:04:14,790
because it's five away
from both elements.

96
00:04:14,790 --> 00:04:17,339
It's five away from 40,
and five away from 30.

97
00:04:17,339 --> 00:04:19,050
So the mathematical
community has

98
00:04:19,050 --> 00:04:21,380
decided to define
what to do in the case

99
00:04:21,380 --> 00:04:23,710
where you have a 5
in the ones place.

100
00:04:23,710 --> 00:04:27,690
If you have five or more in the
ones place, you will round up.

101
00:04:27,690 --> 00:04:28,730
This is just a rule.

102
00:04:28,730 --> 00:04:31,850
Five or more in the ones
place, you round up.

103
00:04:31,850 --> 00:04:35,450
So 35, you round up to 40.

104
00:04:35,450 --> 00:04:39,940
Notice, a 6 in the ones
place was five or more.

105
00:04:39,940 --> 00:04:43,320
So if you're rounding to the
nearest 10, you round up to 40.

106
00:04:43,320 --> 00:04:49,091
A 4 in the ones place is not 5
or greater, so we rounded down.

107
00:04:49,091 --> 00:04:50,590
And so this gives
a pretty good clue

108
00:04:50,590 --> 00:04:52,120
for these other two numbers.

109
00:04:52,120 --> 00:04:56,230
Let's try-- let's see
what happens with 26.

110
00:04:56,230 --> 00:04:58,350
26, what are the two options?

111
00:04:58,350 --> 00:05:00,370
What is a multiple
of 10 above 26,

112
00:05:00,370 --> 00:05:03,810
and what is a multiple
of 10 below 26.?

113
00:05:03,810 --> 00:05:08,460
Well, the multiple
of 10 above 26 is 30,

114
00:05:08,460 --> 00:05:12,400
and the multiple of
10 below 26 is 20.

115
00:05:12,400 --> 00:05:14,030
So if we round up, we go to 30.

116
00:05:14,030 --> 00:05:17,290
If we round down, we go to 20.

117
00:05:17,290 --> 00:05:19,040
Well, if we're rounding
to the nearest 10,

118
00:05:19,040 --> 00:05:20,130
we look at the 10's place.

119
00:05:20,130 --> 00:05:20,980
That's what we're
going to round--

120
00:05:20,980 --> 00:05:22,890
we're going to round
to the nearest 10--

121
00:05:22,890 --> 00:05:24,500
but then we look
at the ones place.

122
00:05:24,500 --> 00:05:26,370
The ones place is
going to decide it.

123
00:05:26,370 --> 00:05:31,510
And we see here this
is 5 or greater.

124
00:05:31,510 --> 00:05:34,410
Or you could say this is
greater than or equal to 5.

125
00:05:34,410 --> 00:05:36,460
So we round up.

126
00:05:36,460 --> 00:05:41,580
26 rounded to the nearest
10, we round up to 30.

127
00:05:41,580 --> 00:05:44,060
Now what about 12?

128
00:05:44,060 --> 00:05:46,480
And I think you're
getting the hang of this.

129
00:05:46,480 --> 00:05:49,750
Well let's think about the
multiple of 10 above 12.

130
00:05:49,750 --> 00:05:51,810
So we could either
round up to 20.

131
00:05:51,810 --> 00:05:54,790
So 12 is sitting
right around here.

132
00:05:54,790 --> 00:05:59,230
We either round up to 20
or we round down to 10.

133
00:05:59,230 --> 00:06:01,430
Well, if we're going to
round to the nearest 10,

134
00:06:01,430 --> 00:06:03,590
we have to look
at the ones place.

135
00:06:03,590 --> 00:06:06,440
We have to look at the
ones place right over here.

136
00:06:06,440 --> 00:06:09,090
This is less than 5.

137
00:06:09,090 --> 00:06:11,670
Since it's less than
five, we round down,

138
00:06:11,670 --> 00:06:13,670
which makes sense because
it's also closer to 10

139
00:06:13,670 --> 00:06:15,020
than it is to 20.

140
00:06:15,020 --> 00:06:19,100
So we round down, and
rounding 12 to the nearest 10,

141
00:06:19,100 --> 00:06:21,610
you actually get 10.