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- What digits could replace[br]the question mark in the

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hundreds place to make[br]this statement true?

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Four thousand question[br]mark hundreds 29 rounds

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to 5000 if we round to[br]the nearest thousand.

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So we want a number whose[br]nearest thousand is 5000.

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It's closer to 5000[br]than any other thousand.

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And what we know about our[br]number so far is it starts

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with 4000 then we'll fill in[br]the digit for the hundreds

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and ends with 29.

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So, we want to know what[br]digits from zero to nine

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can we fill in here so that[br]this number is closer to 5000

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than any other thousand.

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Well the only other[br]thousand this could be close

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to is 4000 because we're[br]starting with a four here,

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all of our numbers will[br]be between 4000 and 5000,

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so let's draw that, let's[br]show that on a number line.

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Here's a number line that[br]goes from 4000 to 5000

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and then the hundreds here[br]are marked so this would

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be 4100, 4200, 4300,

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4400, so on all the way to 4900

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and then finally, 5000.

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So if we want to fill in[br]digits here, then we can

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graph them on our number[br]line and see what are they

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nearest to.

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Are they nearest to 5000 or[br]are they nearest to 4000?

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Just, for example, if we[br]plot a number right here,

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whatever number this point[br]represents, what is its

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nearest thousand?

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Well, it is literally nearest[br]to 5000, so it would round

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to 5000, that would be[br]its nearest thousand.

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But, if for example we had[br]a point that was somewhere

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like this, this points nearest[br]thousand would be 4000.

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This point would round[br]down to 4000 because we can

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look and see, it is closer[br]to 4000 than it is to 5000.

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It is nearer.

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So, let's look back now[br]at our number and try to

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fill in some digits and[br]see where they land on this

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number line.

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Let's draw in the first[br]possible digit we could fill

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in here, is a zero.

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So this would be 4000 zero[br]hundreds 29, well that

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would be between 4000 and[br]4100, it's greater than

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4000 but not quite all the[br]way to 4100, so we could

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put that probably somewhere,[br]estimating a little bit,

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about right here, a little[br]closer to 4000 than 4100.

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And now looking at this[br]number, we can see it is much

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closer to 4000, its nearest[br]thousand is definitely 4000.

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It takes us far longer to get to 5000,

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so zero will not work.

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So, we can take away, it's[br]not going to be a zero.

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And I don't know that we[br]need to try all 10 numbers,

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what we can do is look down[br]here, let's look at this

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graph and see which section[br]of it, which section

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of this number line is closer to 5000.

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And the answer will be if[br]we find right in the middle,

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here, 4500, anything greater than this

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will round up to 5000.

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From the halfway point[br]up will round up to 5000.

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So, what points knowing that this

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right here is 4500,

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what numbers or what[br]digits can we fill in here

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to get a number that's greater than 4500?

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Because anything less than[br]that's going to round down,

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be closer to 4000.

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And so, we could try,[br]let's just put a five in.

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4529 would be right after 4500,

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somewhere about like this, that is closer,

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just barely but it's closer[br]to 5000, so five works.

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Five is a digit that we could use.

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What about four, if we fill[br]in a four here, we have

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4400, well that's going[br]to be just to the left

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of 4500, this line is 4400,

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here's 4500, so that[br]point will come somewhere

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around her, which just barely

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rounds down to 4000, it's[br]close to the middle but

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a little bit closer, a[br]little bit nearer to 4000,

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its nearest thousand is 4000.

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So, four will not work,[br]five does work and from here

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I think we can figure out[br]our solution almost without

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using the number line.

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If 4400 was too small, well then

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4300 is definitely too[br]small and 200 and 100

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and we already saw zero[br]hundreds was way here,

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way down here which is way too

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small, and now we know 4529 works,

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that's big enough, so[br]anything bigger will only

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get closer to 5000.

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Anything bigger than 5[br]int he hundreds place will

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only move us closer,[br]farther to the right, so any

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digit five or greater[br]would work here, would

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round up to 5000.

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So the digits that are[br]five or greater are five,

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and then six, seven, eight and nine.

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Those are the possible digits[br]that we could fill into

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our hundreds place so that[br]our number rounds to 5000

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as its nearest thousand.

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The solutions are five,[br]six, seven, eight and nine.