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Rounding to the nearest 100 on the number line

CCSS Math: 3.NBT.A.1

Video transcript

- [Narrator] At this point, you are likely already familiar with the idea of rounding. Probably, you have had some practice rounding to the nearest 10. Now we're gonna do another type of rounding. We are now going to round to the nearest 100. So let's just start with an example, and you'll see that in a lot of ways, it's very similar to rounding to the nearest 10, we're just looking at different place values now. So let's say we have the number 345. And we want to round this to the nearest 100. So pause this video, and see, I know I haven't even taught you how to do that, but what's your intuition? What is the nearest 100 to 345? Okay, now let's do this together. And what we wanna do is first look at the 100s place. And you can see 345 is three 100s, four 10s, and five ones. So 345, the 100, the number of 100s, that is right below 345 is three 100s, so it's between three 100s, zero 10s, and zero ones, and then the number of 100s that's right above this number is 400. We're in between three 100s and four 100s. And 400. So if we're gonna round this to the nearest 100, it's gonna go to one of these two. Well, to think about which one we round to, we have to think about well, is 345 closer to 400, or is it closer to 300? And to think about that, we can draw ourselves a number line. And so let me just start my number line here at, I'll just start it at 200. So that's 200, let's make this 300, and then this would be 400. And then since we, let's just see, this would be about 350 right over here, so I'll do the 50s right over there. So that 350. So where would 345 sit? Well, 345 is a little bit less than 350. It's going to be roughly right over there. So which 100 is it closer to? Are we closer to 300, or are we closer to 400? Well, you can visually see, 350 is right in between. It's 50 away from 300, and 50 away from 400. So 345 is going to be a little bit closer to 300. So in this situation, if we're rounding to the nearest 100, we would round down to 300. Now another way that you could do this, and it's very similar to what we thought about when we rounded to the nearest 10, is okay, we're rounding to the nearest 100, so this is either going to be rounded to a three or a four, and to decide on that, we go to one place value less than that. So to decide on that, we would go to the 10s place. Let me do this in a different color. Go to the 10s place. And in our 10s place right over here, if this is less than five, then we round down. If it is greater than or equal to five, we round up. So in this situation, it is less than five, so we round down. If this was 365, well then that would be greater than or equal to five, so then we would round up. And that makes sense, because 365 would be over here, and it would be closer to 400. Let's do another example. We'll do it both with what I just described, and we'll do it with a number line. And I'll actually do a four digit number now, just to just mix things up a little bit. Let's say we have the number 7,652. Pause this video, and see if you can round this number to the nearest 100. Alright, now let's do it together. Now, we're thinking about the 100s place, so right over there. You can view this as seven thousands and six 100s. Or you could even view this as 76 100s. So what are the closest 100s to this number? Well, this is, you could either view this as 76 100s and five 10s and two ones, or seven thousands, six 100s, five 10s, and two ones. And so either way, the 100s that are right below this is 76 100s, or 7,600, and the 100s that are right above this, well you would just take one more than this six, so that would be 7700, 7700. And so, which one would it round to? Well, we could use the technique that I just showed you. You go one place value less than the 100s, which in this case is in the 10s position, and you would say, alright, is this greater than or equal to five? If it is, we round up. Is this less than five? Then we round down. This is greater than or equal to five. It's equal to five. So in this situation, we round up to 7700. And we can see that on a number line as well. Let me draw a number line here. And so let me just start at, let's say that this is 7500, this is 7600, or 7,600, and this right over here is 7,700. And this would be 7,650 right over here. And so 7,652 is going to be a little bit more than that. It's going to be a little bit more. And since you can see, it's either right in the middle, or to the right of right in the middle, we would round up to 7700, which is exactly what we just did. Now let me give you another interesting example. Let's say we wanted to round to the nearest 100 for 982. What would that be? Well once again, we look at the 100s place. Well what's 100 that's right below 982? Well if you just get rid of the 82, you're just left with nine 100s, so that would be 900 if you round down. And if you were to round up, what's the 100s right above this? Well, you could go from nine 100s to 10 100s, and that would be the same thing as 1,000. And so I wanted to show this example because when you're rounding up here, the next 100 is 10 100s, or 1,000. And so we can see very clearly here that if we look at the 10s place, the eight is greater than or equal to five, so we are going to round up. So 982 rounded to the nearest 100s is 1,000.