WEBVTT

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Throughout your
mathematical life,

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you will find situations where
you will need to round numbers.

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And you might be
saying, well why?

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What situations might that be?

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Well, these would
be situations where

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you're trying to get
an estimate on things.

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Where you're trying to--
maybe you have a measurement

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and you want it to be a little
bit less exact to simplify

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things.

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Or you don't trust how
exact the measurement is.

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So here we're going to actually
think about what rounding is.

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And we're going to round each of
these numbers, 36, 34, 35, 26,

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and 12.

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We're going to round each
of them to the nearest 10.

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And I'll give you a
hint of what that means.

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That essentially says take
each of these numbers,

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and find the multiple of
10 that it is closest to.

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So what are multiples of 10?

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Well, 10 times 0
is 0, 10 times 1

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is 10, 20, 30, 40, 50,
60, so on and so forth.

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So I encourage you
to pause this video,

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and just based on what I just
told you, what is the nearest

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multiple of 10 to
each of these numbers?

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Try to think about that.

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Well, to think about it a
little bit deeper, let's

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actually put a number line here.

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I'll put two number
lines over here.

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So we've got some
number lines here.

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And let's think about
where these points

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would sit on this number line.

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So this first number,
36, where does it

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sit on this number line?

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Well, it's between 30 and 40.

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And this little blue mark
is 35, it's halfway between.

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So 36 is going to be a
little higher than that.

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So 36 is going to
be right over here.

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And if we zoom in
between 30 and 40.

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So if we say that this
is 30, and this is 40,

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where is 36 going to be?

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So once again, this is 35.

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36 is one notch above that.

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So 36 is going to
be right over here.

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So if we want to round to the
nearest 10, to the nearest

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multiple of 10, what are
the two possibilities here?

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Well, I could take 36
and I could round up

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to the multiple of 10
above it, which is 40.

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So I could round up to
40, or I could round down

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to the multiple of 10
below it, which is 30.

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And so I need to figure
out which of these numbers

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is it closer to.

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Well, when you just look at
that, even just eyeballing it,

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you can see it.

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But you could also say 36
is only four away from 40,

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and it's six away from
30, it's closer to 40.

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So we are going to round up.

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We are going to round up to 40.

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This is literally
called rounding up.

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Now let's try some of
these other numbers.

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What about 34?

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And I encourage you
to pause the video.

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Think about what
number you would

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get if you were to try to
round it up or round it down,

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and then which one it
is actually closer to.

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Well, 34 is right over
here on this number line,

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where we zoom in, 34
is right over here.

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And we have two options.

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The multiple of
10 above 34-- let

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me do those same colors-- the
multiple of 10 above 34 is 40.

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Multiple of 10 below
34, again, is 30.

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Now, which one is it closer to?

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Well it's only four away from
30, and six away from 40,

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so it's closer to 30.

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So we are going to
round down to 30.

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And notice we went to 30.

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You might say, hey,
when we rounded it

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up the 10's place increased
from 3 to 4, from 30 to 40.

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Maybe when we round
down, the 10's place

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will decrease from
30 to 20, but no, 30

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is the multiple of 10 below 34.

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So when you round
down, you just go--

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you keep the multiple of 10,
but the ones place becomes a 0.

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Now let's try a really
interesting one.

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Let's think about rounding the
number 35 to the nearest 10.

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And first, before we
even try to do it,

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let's think about
the two options.

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Well, we've already seen it.

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35 is sitting right over here.

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On this number line, that
is 35, and once again we

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have two options.

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35, we can round it up to 40,
or we could round it down to 30.

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And I encourage you to pause
the video and think about this.

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Well this one is a
little bit of a conundrum

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because it's five away
from both elements.

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It's five away from 40,
and five away from 30.

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So the mathematical
community has

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decided to define
what to do in the case

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where you have a 5
in the ones place.

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If you have five or more in the
ones place, you will round up.

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This is just a rule.

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Five or more in the ones
place, you round up.

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So 35, you round up to 40.

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Notice, a 6 in the ones
place was five or more.

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So if you're rounding to the
nearest 10, you round up to 40.

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A 4 in the ones place is not 5
or greater, so we rounded down.

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And so this gives
a pretty good clue

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for these other two numbers.

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Let's try-- let's see
what happens with 26.

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26, what are the two options?

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What is a multiple
of 10 above 26,

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and what is a multiple
of 10 below 26.?

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Well, the multiple
of 10 above 26 is 30,

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and the multiple of
10 below 26 is 20.

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So if we round up, we go to 30.

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If we round down, we go to 20.

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Well, if we're rounding
to the nearest 10,

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we look at the 10's place.

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That's what we're
going to round--

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we're going to round
to the nearest 10--

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but then we look
at the ones place.

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The ones place is
going to decide it.

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And we see here this
is 5 or greater.

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Or you could say this is
greater than or equal to 5.

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So we round up.

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26 rounded to the nearest
10, we round up to 30.

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Now what about 12?

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And I think you're
getting the hang of this.

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Well let's think about the
multiple of 10 above 12.

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So we could either
round up to 20.

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So 12 is sitting
right around here.

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We either round up to 20
or we round down to 10.

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Well, if we're going to
round to the nearest 10,

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we have to look
at the ones place.

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We have to look at the
ones place right over here.

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This is less than 5.

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Since it's less than
five, we round down,

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which makes sense because
it's also closer to 10

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than it is to 20.

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So we round down, and
rounding 12 to the nearest 10,

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you actually get 10.