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Rounding to the nearest 10 on the number line

CCSS Math: 3.NBT.A.1

Video transcript

- [Instructor] In this video, we're going to be doing some rounding, which you're probably not familiar with just yet but you'll see that it's pretty straightforward and we're going to start by rounding to the nearest 10. So the first question is, what is rounding and why is it even useful? Well, let's say that you have the number 37. It's a fine number. But let's say that you have to do some math with the number 37 and you can do a lot of math with the number 37. But let's say you just wanna estimate what something might be. Let's say that if someone says, hey, I have 37 pickles and you have 39 pickles, roughly, how many do we have together? We don't have to have it down to the exact number of pickles. Well then, rounding will actually be a very useful tool. But let's just focus on what it means to round to the nearest 10. So when they're talking about rounding to the nearest 10, we're gonna be thinking about the tens place of the number. So we can see right over here in our tens place, we have a three. And so that three represents three tens. So the number 37, it's three tens and seven ones, so it is more than three tens and it's gonna be less than four tens. So this number is going to be more than three tens, I could do it like this. It's gonna be more than three tens, which we can represent like that, three tens and zero ones, or you might know that as 30, and it's going to be less than four tens or also known as 40. And so, when you're rounding, you're either going to round to the number of tens that is right below this number or the number of tens that is right above that. But how do we know whether 37 rounded to the nearest 10 is going to be 30 or 40? Well, to answer that question, let's first just do it visually on a number line. And then we can come up with some rules for ourselves. And so, first of all, let's just count by tens and we make sure we include 30 and 40. So, if we start at zero, 10, 20, actually, let me have a little bit more space 'cause I wanna see the interesting things that are going to go on. Zero, 10, 20, 30, 40, that's enough, but I could just go to 50 just to complete this number line. And so, where is 37 on this number line? Well, it's between 30 and 40, and if I wanted to make it a little bit clear, if I said that this is 35 right over there, right in between 30 and 40, then 37 is going to be right about, right about here. So, that is 37. And so, when you're rounding to the nearest 10, and remember, we're picking between three tens and four tens, you say which 10 is it closest to. Is it closer to three tens or is it closer to four tens? Well, you can just look at this and say, hey, it looks a lot closer to four tens. And so in this situation, 37 rounded to the nearest 10 is going to be 40. And so, you might ask a question, well, give me another number. What if someone said 32 rounded to the nearest 10? Well, 32 is going to be right over here. And then you'd say, all right, well, that's between three tens and four tens, but it's a lot closer to three tens, so 32 rounded to the nearest 10 is going to be, is going to be 30. Now, an interesting question that you might be wondering is what if you're right in between? What if we wanted to round 35 to the nearest 10? 35, once again, it's between three tens and four tens, between 30 and 40. Which one do we round to if we wanna round to the nearest 10? Well, the rule is, and this is really just something that the society has decided on is that if you're right in the middle, you round up, so the number 35 is going to round up to 40. Even though it's exactly five away from each of these numbers, 35, if you're right in between, is going to round up to 40. If you're a little bit less than 35, then you're going to round down to 30. With that out of the way, let's do some more examples. Let's do, actually, let's do an example of a three-digit number, where we're rounding to the nearest 10. Let's say that we want to round the number 124 to the nearest 10. Well, there's a couple of ways that you could think about this. You could say that this is 100, two tens and four ones. Or you could even view this as 12 tens and four ones. So you could say, hey, this is in between, 12 tens and four ones, it's greater than 12 tens, which is 120, and it's less than 13 tens, which is 130. These are the two tens that are closest to this number. And then to decide which one it rounds to, you might already be able to think about it based on some of the rules we came up with, but let me draw it on a number line for you. So we draw a number line, and I'm not going to start at zero, because we have to get all the way to 130, so let's just start, I'll start at a hundred. So, this is 100, 110, let me draw the number line, we're going to have 120, then we go to 130. I'll just do 140 here just for filling out the number line that I've drawn so far. And then I'll draw the halfway mark, which is 125. And then, see its halfway, so maybe a little bit closer to there. And then 124, we do it in this red color, 124 is right over there. 124. And so, if we're trying to pick between 120 and 130, between 12 tens and 13 tens, which one is it closer to? Well, we can see it's only four away from 120 while it's six away from 130, so we would round down, we're going to round down to 120 in this situation if we're rounding to the nearest 10. If this was 125 or 126 or 127 or 128 or 129, well then, we would round to 130. And of course, if it was 130, we would round it to 130. Let's do one more example. And actually, I'm going to do a one-digit number. Let's say we wanna round seven to the nearest 10. I'll write it out, round seven to the nearest, nearest 10. Pause this video and see if you can do that. All right, well, seven is between what two tens? Well, seven is less than one ten, so it's less than one ten, and it's greater than zero tens. So, it's between zero tens, which is just zero, and one ten, which is 10, but which one does it round to? Well here, once again, we can draw our number line. So, we'll do zero and then this is five and then this is 10, and seven is right about there. That is where seven is. And we can either visually see that seven is closer to 10 than it is to zero. It's only three away from 10 while it's seven away from zero, so you would round up to 10. Or you can use the rule that we just thought about. Seven is greater than or equal to five, so you round up. You round to the 10 that is higher than this number. If this number was, if in this ones place, I can say, if your ones place is between zero, it's greater than or equal to zero but less than five, then you round down. And you can see that happens in all of these situations. If you look at 37, you look at the ones place and your ones place here is greater than or equal to five, so you round up. Here, if your ones place, it's greater than or equal to five, it's five exactly in that situation, so it's equal to five, once again, you round up. If your ones place is less than five, well, in this situation, we round down. If your ones place is less than five, you round down. Your ones place, and here, you only have a ones place, but it's greater than or equal to five, we round it up.