Rounding to the nearest 10

Throughout your
mathematical life,

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

And you might be
saying, well why?

What situations might that be?

Well, these would
be situations where

you're trying to get
an estimate on things.

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

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

things.

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

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

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

and 12.

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

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

That essentially says take
each of these numbers,

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

So what are multiples of 10?

Well, 10 times 0
is 0, 10 times 1

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

So I encourage you
to pause this video,

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

multiple of 10 to
each of these numbers?

Try to think about that.

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

actually put a number line here.

I'll put two number
lines over here.

So we've got some
number lines here.

And let's think about
where these points

would sit on this number line.

So this first number,
36, where does it

sit on this number line?

Well, it's between 30 and 40.

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

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

So 36 is going to
be right over here.

And if we zoom in
between 30 and 40.

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

where is 36 going to be?

So once again, this is 35.

36 is one notch above that.

So 36 is going to
be right over here.

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

multiple of 10, what are
the two possibilities here?

Well, I could take 36
and I could round up

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

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

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

And so I need to figure
out which of these numbers

is it closer to.

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

you can see it.

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

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

So we are going to round up.

We are going to round up to 40.

This is literally
called rounding up.

Now let's try some of
these other numbers.

What about 34?

And I encourage you
to pause the video.

Think about what
number you would

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

and then which one it
is actually closer to.

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

where we zoom in, 34
is right over here.

And we have two options.

The multiple of
10 above 34-- let

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

Multiple of 10 below
34, again, is 30.

Now, which one is it closer to?

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

so it's closer to 30.

So we are going to
round down to 30.

And notice we went to 30.

You might say, hey,
when we rounded it

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

Maybe when we round
down, the 10's place

will decrease from
30 to 20, but no, 30

is the multiple of 10 below 34.

So when you round
down, you just go--

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

Now let's try a really
interesting one.

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

And first, before we
even try to do it,

let's think about
the two options.

Well, we've already seen it.

35 is sitting right over here.

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

have two options.

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

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

Well this one is a
little bit of a conundrum

because it's five away
from both elements.

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

So the mathematical
community has

decided to define
what to do in the case

where you have a 5
in the ones place.

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

This is just a rule.

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

So 35, you round up to 40.

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

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

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

And so this gives
a pretty good clue

for these other two numbers.

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

26, what are the two options?

What is a multiple
of 10 above 26,

and what is a multiple
of 10 below 26.?

Well, the multiple
of 10 above 26 is 30,

and the multiple of
10 below 26 is 20.

So if we round up, we go to 30.

If we round down, we go to 20.

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

we look at the 10's place.

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

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

but then we look
at the ones place.

The ones place is
going to decide it.

And we see here this
is 5 or greater.

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

So we round up.

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

Now what about 12?

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

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

So we could either
round up to 20.

So 12 is sitting
right around here.

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

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

we have to look
at the ones place.

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

This is less than 5.

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

which makes sense because
it's also closer to 10

than it is to 20.

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

you actually get 10.