Rounding whole numbers: missing digit | Math | 4th grade | Khan Academy

What digits could replace the question mark in the hundreds place to make this statement true?

4,000 question mark hundreds 29 rounds to 5,000 if we round to the nearest thousand. So we want a number whose nearest thousand is 5,000. It's closer to 5,000 than any other thousand. What we know about our number so far is it starts with 4,000, then we'll fill in the digit for the hundreds, and it ends with 29.

So, we want to know what digits from 0 to 9 can we fill in here so that this number is closer to 5,000 than any other thousand. Well, the only other thousand this could be close to is 4,000 because we're starting with a four here. All of our numbers will be between 4,000 and 5,000.

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 4,100, 4,200, 4,300, 4,400, and so on, all the way to 4,900, and then finally 5,000.

If we want to fill in digits here, then we can graph them on our number line and see what they are nearest to. Are they nearest to 5,000 or are they nearest to 4,000? 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 5,000, so it would round to 5,000; that would be its nearest thousand.

But if, for example, we had a point that was say somewhere like this, this point's nearest thousand would be 4,000. This point would round down to 4,000 because we can look and see it is closer to 4,000 than it is to 5,000; 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 fill in the first possible digit we could fill in here as a zero, so this would be 4,029. 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 place that probably somewhere just estimating a little bit about right here, a little closer to 4,000 than 4,100.

Now, looking at this number, we can see it is much closer to 4,000. Its nearest thousand is definitely 4,000; it takes far longer to get to 5,000, 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 5,000.

The answer would be, if we find right in the middle here 4,500, anything greater than this will round up to 5,000. From the halfway point up, we’ll round up to 5,000.

So what points, knowing that this right here is 4,500, what numbers or what digits could we fill in here to get a number that's greater than 4,500? Because anything less than that's going to round down and be closer to 4,000.

So we could try 4,500. Let’s just put a five in; 4,529 would be right after 4,500. Somewhere about like this, that is closer, just barely, but it's closer to 5,000, so five works. Five is a digit that we could use.

What about four? If we fill in a four here, we have 4,400. Well, that’s going to be just to the left of 4,500. This line is 4,400; here's 4,500. So that point will come somewhere around here, which just barely rounds down to 4,000.

It's close to the middle, but a little bit closer, a little bit nearer to 4,000. Its nearest thousand is 4,000, 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 4,400 was too small, well then 4,300 is definitely too small, and 200 and 100. We already saw 0 hundreds was way here, way down here, which is way too small.

Then we know 4,529 works; that’s big enough, so anything bigger will only get closer to 5,000. Anything bigger than five in the hundreds place will only move us closer, farther to the right.

So any digit five or greater would work here, would round up to 5,000. 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 5,000 as its nearest thousand. The solutions are 5, 6, 7, 8, and 9.