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# Rounding to nearest 100

Video transcript

We're asked to round 152, 137,
245, and 354 to the nearest 100, which is another
way of saying round each of these numbers to the
nearest multiple of 100. So let's think about
them one by one. So let's draw a
number line here. And here I'm counting
up by hundreds. What I've marked here,
100, 200, 300, 400, these are all multiples of 100. I could keep going up. I could go to 500, 600,
so on and so forth. Now, let's start with 152. Well, where does 152 sit? So halfway in between is 150. 152 is going to be right
to the right of that. So that's 152 right over here. So what are our two options? We might round up. The multiple of 100
above 152 is 200. The multiple of 100
below 152 is 100. So which direction do we go in? Do we round up to 200, or
do we round down to 100? Well, if we're rounding
to the nearest 100, we want to look at one
place to the right of that. We want to look
at the tens place to decide which multiple
of 100 it is closer to. And the rules are
very similar to when we're rounding to the nearest
tens place or really any place. We look one place
to the right of it. So in this case, we
look at the tens place. And we say, if this is 5
or larger, we round up. And this is 5 or larger, so
we're going to round up to 200. So this we're going to round. 152, we're going to round to
200, which also makes sense. 152 is a little
bit closer to 200. It's 48 away from to
200 than it to 100. It's 52 away from 100. So it makes sense to go up to
the nearest multiple of 100. Now, let's think about 137. And I encourage you
to now pause the video and try to round each of
these other three numbers to the nearest 100. Well, 137 is going to sit
someplace right over here. 137 is going to be
right over there. So two options-- we
can round down to 100. That's the multiple
of 100 below 137. Or we could round up to 200. Well, 137, just looking at
it, is clearly closer to 100. Or we could apply our rule. If we're rounding
to the nearest 100, we want to look at one
place to the right of that. We want to look
at the tens place. If this is 5 or
larger, we round up. If it's less than
5, we round down. So in this case, we
would round down to 100. Let's do the same
thing with 245. If you haven't paused it
and tried it yourself, once again, I want to emphasize. That'll make it really valuable
for you to try it on your own. So let's plot where 245 is. So 245 is right
around-- this is 250, so 245 might be
right around here. Now, let's apply that rule. If we're trying to round
to the nearest 100, we would look to one
place to the right. We'll look at the tens place. We could ignore the ones place. We look at the tens place here. If it is greater than or
equal to 5, we round up. If it is less than
5, we round down. So here, we're clearly
going to round down. And when we round
down, we're going to round down to the multiple of
100 that's directly below 245. Well, we're going to
round down to 200. We had two options. If we rounded up, we
would have gone to 300. If we rounded down,
we would go to 200. We're clearly closer to 200. And we can verify
that with the rule. The tens place, we're
in the 40's here. The tens place is a 4. We're going to round down. Now let's think about 354. If we were to plot
that, this is 350. 354 might be right over here. So if we rounded down,
we would go to 300. If we rounded up,
we would go to 400. Now let's apply our
rule, and let's also think about it on
the number line. This is all about finding
the multiple of 100 that it's closest to. If you're trying to
round to the nearest 100, you want to look at
the tens place, a place to the right of the
place you're rounding to. If the tens place
is a 5 or larger, you're going to round up. This is a 5 or larger so we're
going to round up to 400. And that also makes sense. The rule is really valuable. If you're right at
350, right in between, then you would need the rule to
say, hey, let's look at this 5 and round up. But 354 is also closer
to 400 than it is to 300. It's 54 away from 300. It's 46 away from 400. So it makes sense that
we would round up to 400.