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## Rounding whole numbers

# Rounding whole numbers: missing digit

CCSS.Math:

## Video transcript

- What digits could replace
the question mark in the hundreds place to make
this statement true? Four thousand question
mark hundreds 29 rounds to 5000 if we round to
the nearest thousand. So we want a number whose
nearest thousand is 5000. It's closer to 5000
than any other thousand. And what we know about our
number so far is it starts with 4000 then we'll fill in
the digit for the hundreds and ends with 29. So, we want to know what
digits from zero to nine can we fill in here so that
this number is closer to 5000 than any other thousand. Well the only other
thousand this could be close to is 4000 because we're
starting with a four here, all of our numbers will
be between 4000 and 5000, so let's draw that, let's
show that on a number line. Here's a number line that
goes from 4000 to 5000 and then the hundreds here
are marked so this would be 4100, 4200, 4300, 4400, so on all the way to 4900 and then finally, 5000. So if we want to fill in
digits here, then we can graph them on our number
line and see what are they nearest to. Are they nearest to 5000 or
are they nearest to 4000? Just, for example, if we
plot a number right here, whatever number this point
represents, what is its nearest thousand? Well, it is literally nearest
to 5000, so it would round to 5000, that would be
its nearest thousand. But, if for example we had
a point that was somewhere like this, this points nearest
thousand would be 4000. This point would round
down to 4000 because we can look and see, it is closer
to 4000 than it is to 5000. It is nearer. So, let's look back now
at our number and try to fill in some digits and
see where they land on this number line. Let's draw in the first
possible digit we could fill in here, is a zero. So this would be 4000 zero
hundreds 29, well that would be between 4000 and
4100, it's greater than 4000 but not quite all the
way to 4100, so we could put that probably somewhere,
estimating a little bit, about right here, a little
closer to 4000 than 4100. And now looking at this
number, we can see it is much closer to 4000, its nearest
thousand is definitely 4000. It takes us far longer to get to 5000, so zero will not work. So, we can take away, it's
not going to be a zero. And I don't know that we
need to try all 10 numbers, what we can do is look down
here, let's look at this graph and see which section
of it, which section of this number line is closer to 5000. And the answer will be if
we find right in the middle, here, 4500, anything greater than this will round up to 5000. From the halfway point
up will round up to 5000. So, what points knowing that this right here is 4500, what numbers or what
digits can we fill in here to get a number that's greater than 4500? Because anything less than
that's going to round down, be closer to 4000. And so, we could try,
let's just put a five in. 4529 would be right after 4500, somewhere about like this, that is closer, just barely but it's closer
to 5000, so five works. Five is a digit that we could use. What about four, if we fill
in a four here, we have 4400, well that's going
to be just to the left of 4500, this line is 4400, here's 4500, so that
point will come somewhere around here, which just barely rounds down to 4000, it's
close to the middle but a little bit closer, a
little bit nearer to 4000, its nearest thousand is 4000. So, four will not work,
five does work and from here I think we can figure out
our solution almost without using the number line. If 4400 was too small, well then 4300 is definitely too
small and 200 and 100 and we already saw zero
hundreds was way here, way down here which is way too small, and now we know 4529 works, that's big enough, so
anything bigger will only get closer to 5000. Anything bigger than 5
int he hundreds place will only move us closer,
farther to the right, so any digit five or greater
would work here, would round up to 5000. So the digits that are
five or greater are five, and then six, seven, eight and nine. Those are the possible digits
that we could fill into our hundreds place so that
our number rounds to 5000 as its nearest thousand. The solutions are five,
six, seven, eight and nine.