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CCSS Math: 4.NBT.A.3

Round 24,259 to the
nearest hundred. You're going to find that
doing these problems are pretty straightforward, but
what I want to do is just think about what it means to
round to the nearest hundred. So what I'm going to do is I'm
going to draw a number line. Let me draw a number line here,
and I'm just going to mark off the hundreds
on the number line. So maybe we have 24,100, and
then we go to 24,200, then we go to 24,300, and then
we go to 24,400. I think you see what I
mean when I'm only marking off the hundreds. I'm going up by increments
of 100. Now, on this number line,
where is 24,259? So if we look at the number
line, it's more than 24,200 and it's less than 24,300. And it's 259, so if this
distance right here is 100, 59 is right about there, so that
is where our number is. That is 24,259. So when someone asks you to
round to the nearest hundred, they're literally saying round
to one of these increments of 100 or round to whichever
increment of 100 that it is closest to. And if you look at it right like
this, if you just eyeball it, you'll actually see that it
is closer to 24,300 than it is to 24,200. So when you round it,
you round to 24,300. So if you round to the nearest
hundred, the answer literally is 24,300. Now that's kind of the
conceptual understanding of why it's even called the
nearest hundred. The nearest hundred is 24,300. But every time you do a problem
like this, you don't have to draw a number line and
go through this whole process, although you might want
to think about it. An easier process, or maybe a
more mechanical process, is you literally look at
the number 24,259. We want to round to the nearest
hundred, so you look at the hundreds place. This is the hundreds place right
here, and when we round, that means we don't
want any digits. We only want zeroes after
the hundreds place. So what you do is you look at
the place one less than the place you're rounding to. This is the hundreds place so
you look at the 5 right there, and if this number is 5 or
greater, if it's 5, 6, 7, 8, or 9, you round up. So 5 or greater, you round up. And so rounding up in this
situation, it is 5. It is 5 or greater, so rounding
up means that we go to 24,000, and since we're
rounding up, we make the 2 into a 3. We increment it by one, so
rounding up, so 24,300. That's what we mean
by rounding up. And just as kind of a
counterexample, if I had 24,249 and I wanted to round
to the nearest hundred, I would say, OK, I want to round
to the nearest hundred. Let me look at the tens
place, this place one level to the right. It is not 5 or greater,
so I will round down. And when you round
down, be careful. It doesn't mean you
decreases this 2. It literally means you
just only have the 2. Just get rid of everything
after it. So it becomes 24,200. That's the process where
you round down. If you round up, it
becomes 24,300. And it makes sense. 24,249 is going to be sitting
right over here someplace, so it's going to be closer
to 24,200. 24,200 would be the nearest
hundred when we round down in this case. For the case of the problem,
24,259, the nearest hundred is 24,300. We round up.