Rounding whole number word problems

0:00- [Instructor] If we're told a national park rounded the number of cars entering the park on a given date of 6,780 cars, how many cars could have entered the park if they rounded the number to the nearest 10? Choose all the answers that apply. So pause this video, try to solve this yourself before we solve this together.

0:21Okay, so there's a couple of ways we could think about it. We could think about all of the numbers that, if you round to the nearest 10, would round to 6,780, or we could round each of these to the nearest 10, or we could do some type of a combination. Actually, let's do a little bit of a combination here.

0:36So let's draw a number line, and so if this right over here is 6,780, and I'm going to go up by 10 and down by 10, since we're rounding to the nearest 10, so if we go up by 10, this would be 6,790, and if we go down by 10, this would be 6,000, I should put a decimal there, I should put a comma, 6,770.

1:04Now, before I even look at these choices, what's going to round to 6,780? Well, if I get to 6,775 right over here, so this right over here is 6,775, that would round up, if we're rounding to the nearest 10, to 6,780. It's right in between, but the convention, the rule is that we round up, and actually, let me make it, I know that this isn't exact, since I'm drawing it, but lemme make it a little bit closer to the middle right over here.

1:34So if we're right there, if we're right there at 6,775, that's going to round up to 6,780, and that's going to be true all the way up to, but not including, and lemme put an open circle here, this right over here is 6,785. So 6,785 would round up to 6,790, but if you're right below that, even just a little bit below, you would round down to 6,780.

2:05So let's look at these choices and think about which of these are on this orange part of the number line. So 6,778 cars. Well, that's going to be right around there, and so we clearly see here that it's in that orange. It's much closer to 6,780 than it is to 6,770, so this one works.

2:27It would round to 6,780. What about 6,774 cars? Well, that's right over here. Actually, lemme do this in a different color so we can keep track of things, so this one is right over here, and you could visually see, or you can numerically see, it's closer to 6,770 than 6,780.

2:47It's also out of this orange area that we talked about, so we can rule this one out, and then last but not least, 6,783 is right around there, and we could see that the two choices, you could round down to 6,780 or round up to 6,790, but it's much closer to 6,780.

3:04It's also in this orange area. It doesn't even quite get halfway yet, so this one also would round to 6,780. Let's do another example problem involving rounding. So this one tells us that a school fundraiser collects $3,152. Round the money to the nearest hundred, so again, pause the video and try to work this out.

3:29Well, the way I'm going to do it is I'm gonna set up a number line again, and I'm going to, if I think about the hundreds around this, I could go the nearest hundred below this is 3,100, so this is 3,100, I guess we're talking about dollars, and then the hundreds above this is 3,200, so I'll put that here, so this is $3,200.

3:56Now, we're looking at 3,152, which is gonna be a little bit more than halfway towards 3,200, so that might already show you the direction we're going in, but just to make sure we know what's going on, if we go anywhere, if we're above 3,100 up to, but not including 3,150, so right over here, right over here, these are the things, and there'll be some stuff below here, but this is the stuff that would- And this is 3,150, which is right in between.

4:33If we're at 3,150, you don't round down, you round up to 3,200, but if you're at all below that, if you're at 3,149, you would round down to the nearest hundred, down to 3,100. Now, this number is clearly larger than that. 3,152 is going to be right over here.

4:53It's a little bit larger, so this one is going to be a little bit more than halfway from 3,100 to 3,200, and you could also see it's larger than 3,150, and we would round anything from 3,150 all the way to 3,200, almost to 3,250, but not quite 3,250, we would round that to 3,200, and so round the money to the nearest hundred, this would be 3,200.

5:17If you wanna think about it visually, whichever hundred it's closer to, and this is a little bit closer to 3,200 than it is to 3,100, and if you're right in between, if you're at 3,150, the rule is, the convention that mathematicians have created, is that you would round up, but this isn't even right in between.

5:33It's a little bit closer to 3,200.