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CCSS.Math:

what digits could replace the question mark in the hundreds place to make this statement true 4000 question mark hundreds 29 rounds to five thousand if we round to the nearest thousand so we want a number whose nearest thousand is five thousand it's closer to five thousand than any other thousand and what we know about our number so far is it starts with four thousand then we'll fill in the digit for the hundreds and ends with twenty nine so we want to know what digits from 0 to 9 can we fill in here so that this number is closer to five thousand than any other thousand well the only other thousand this could be close to is four thousand because we're starting with a four here all of our numbers will be between 4,000 and 5,000 so let's draw that let's show that on a number line here's a number line that goes from 4,000 to 5,000 and then the hundreds here are marked so this would be four thousand one hundred four thousand two hundred four thousand three hundred four thousand four hundred so on all the way to four thousand nine hundred and then finally five thousand so if we want to fill in digits here then we can graph them on our number line and see what are they nearest - are they nearest to 5,000 or are they nearest to 4000 just to look at an 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 say somewhere like this this points nearest thousand would be four thousand this point would round down to four thousand because we can look and see it is closer to four thousand than it is to five thousand it is nearer so let's look back now at our number and try to fill in some did it's and see where they land on this number line let's fill in the first possible digit we could fill in here as a zero so this would be four thousand zero hundreds twenty-nine well that would be between 4,000 and 4,100 it's greater than 4,000 but not quite all the way to 4,100 so we could plot that probably somewhere estimating a little bit about right here a little closer to four thousand and four thousand one hundred and now looking at this number we can see it is much closer to four thousand its nearest thousand is definitely four thousand it takes far longer to get to five thousand 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 five thousand and the answer will be if we find right in the middle here four thousand five hundred anything greater than this will round up to five thousand from the halfway point up we'll round up to five thousand so what points knowing that this right here is four thousand five hundred what numbers are what digits could 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 4,000 and so we could try four thousand let's just put a five in four thousand five hundred twenty nine would be right after four thousand five hundred somewhere about like this that is closer just barely but it's closer to five thousand so five works five is a digit that we could use what about for if we fill in a four here we have four thousand four hundred well that's going to be just to the left of 4500 this line is four thousand four hundred here's 4000 five hundred so that point will come somewhere around here which just barely rounds down to four thousand it's close to the middle but a little bit closer a little bit nearer to four thousand its nearest thousand is four thousand so four will not work five does work and from here I think we can figure out our solution almost without even using the number line if four thousand four hundred was too small well the four thousand three hundred is definitely too small and two hundred and one hundred and we already saw zero hundreds was way here way down here which is way too small and then we know five thousand four thousand five hundred twenty nine works that's big enough so anything bigger will only get closer to five thousand anything bigger than five in the hundreds place only move us closer farther to the right so any digit five or greater would work here would round up to five thousand 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 five thousand as its nearest thousand the solutions are five six seven eight and nine