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## Topic C: Foundations

# Rounding to nearest 10 and 100

CCSS.Math:

## Video transcript

We've got four numbers here. What I want to do is try
to round each of these to the nearest 10 and
to the nearest hundred. So I encourage you to pause the
video and try that right now. So let's make two columns. Let's make one first
for the nearest 10 and then make another
column for the nearest 100. And let's start with 154. So 154, what is the
multiple of 10 above 154? Well, it's 160. And the multiple of
10 below 154 is 150. So we're going to round
up to 160 or down to 150. Well, when we're rounding
to the nearest 10, we need to look
at the ones place. One place to the right of the
place that we're rounding. So we look at this
4 in the ones place. Since 4 is less than 5,
we round down to 150. Now, let's think about
that same number, rounding to the nearest hundred,
so 154 to the nearest hundred. So now we need to think
about if we were to round up, what's the multiple
of 100 above 154? 160 isn't the multiple of 100
The multiple of 100 above 154 is 200. What's the multiple
of 100 below 154? Well, that's going to be 100. So if we're going to round
to the nearest hundred-- so we look at the hundreds place. We'll look one
place to the right of that, which is
the tens place. If that place is 5 or
greater, we round up. If it's less than
5, we round down. Well, this is clearly 5
or greater so we round up. So this is interesting. When we rounded to the
nearest 10, since we had a 4 in the ones place,
we rounded down. But when rounded to
the nearest hundreds, since we had a 5 in the tens
place, we rounded up to 200. Let's do some more of these. This is fun. So 4,674. The multiple of 10
above that is 4,680. The multiple of 10
below that, 4,670. Remember, we're concerned
only with the multiple of 10. So do we round up or down? Well, we're thinking about
rounding the tens place. So that's why it's either going
to be an 8 if we round up, or a 7 if we round down. To figure that out, we
look at the ones place. If the ones place is 5
or greater, we round up. If it's less than
5, we round down. It's, once again, less than
5, so we round down to 4,670. Now let's round the same
number to the nearest hundred. What's the multiple
of 100 below this? Well, the multiple of
100 below this is 4,600. The multiple of 100
above this is 4,700. If we're trying to think
about rounding to the nearest hundred, we want to
look at the tens place. The tens place is 5 or greater,
so we round up to 4,700. Now let's tackle 9,995. And once again,
always try to pause these, if you haven't
done so already, to try to do this on your own. So 9,995. What is the multiple
of 10 below this. Well the multiples of
10 below this is 9,990. And what's the multiple
of 10 above this? Well, if you increase this by
10, you actually get to 10,000. So you might say, hey, well
isn't this a multiple of 100, and actually this is a
multiple of a thousand-- it's also a multiple of 10,000. It's all of those,
but the multiple of 10 right above
9,995 is 10,000. You just have to add a little
bit to this to get to 10,000. Or the multiple of 10
below it is clearly 9,990. 10 more than that
gets you to 10,000. So how do we around this? Well, once again, if we're
rounding to the nearest 10, we want to look
at the ones place. The ones place is 5 or greater
so we round up to 10,000. Now, let's round to
the nearest hundreds. You should be getting
used to this now. To the nearest hundreds, what
is the hundreds below this? Well, it's 9,900. What is 100 above this, the
next multiple of 100 above this? Well, if you add 100 to 9,900
you once again get 10,000. So how do we decide whether
to round up or down? Well, we don't look at
the ones place anymore. We're now rounding to
the nearest hundred. So we want to round to
the nearest hundred. To do that, we look
one place to the right, which is the tens place. If this is 5 or
greater, we round up. If it's less than
5, we round down. It is 5 or greater so once
again we round up to 10,000. Now we have one more, 8,346. The multiple of 10
below it is 8,340. Multiple of 10
above that is 8,350. If we're going to round
to the nearest 10, we need to look
at the ones place. The ones place is 5 or
greater, so we round up. Now, let's round to
the nearest hundred. 8,346, the multiple of
100 above this is 8,400. The multiple of 100
below this is 8,300. Notice we're rounding
to the nearest hundreds. If we were to round up, the
hundreds place becomes a 4. If we round down, the
hundreds place stays at 3, but it's followed by zeroes. If we want to round to
the nearest hundreds, we need to look
at the tens place. The tens place here is less than
5, so we round down to 8,300. Notice, again, when we
round to the nearest tens, we rounded up to 8,350. When we round to the
nearest hundreds, we rounded down to 8,300.