Rounding to the nearest 100

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 going to 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. What we want to do is first look at the hundreds place. You could see 345 is three hundreds, four tens, and five ones. So, 345, the number of hundreds that is right below 345 is three hundreds. So, it's between three hundreds, zero tens, and zero ones. And then the number of hundreds that's right above this number is four hundred. We're in between three hundreds and four hundreds.

So, if we're going to round this to the nearest hundred, it's going to 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. 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 draw the 50s right over there, so that's 350. So, where would 345 sit? Well, 345 is a little bit less than 350. It's going to be right, 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 350, 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 hundred, 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 hundred, so this is either going to be rounded to a three or a four.

To decide on that, we go to one place value less than that. So, to decide on that, we would go to the tens place. We do this in a different color. Go to the tens place, and in our tens place, right over here, if this is less than 5, then we round down. If it is greater than or equal to 5, we round up.

So, in this situation, it is less than 5, so we round down. If this was 365, well, then that would be greater than or equal to 5, so 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 mix things up a little bit. Let's say we have the number seven thousand six hundred. Pause this video and see if you can round this number to the nearest 100.

All right, now let's do it together. Now, we're thinking about the hundreds place. So, right over there, you could view this as seven thousands and six hundreds, or you could even view this as seventy-six hundreds. So, what are the closest hundreds to this number?

Well, you could either view this as seventy-six hundreds, five tens, and two ones, or seven thousand six hundreds, five tens, and two ones. And so, either way, the hundreds that are right below this is seventy-six hundreds, or seven thousand six hundred. And the hundreds that are right above this, well, you would just take one more than this six, so that would be seventy-seven hundred—seventy-seven hundred.

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 hundreds, which in this case is in the tens position. And you'd say, all right, is this greater than or equal to five? If it is, we round up. Is this less than 5? Then we round down. This is greater than or equal to 5; it's equal to 5, 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. So, let me just start at—let's say that this is 7500, this is 7600, or seven thousand six hundred, and this right over here is seven thousand seven hundred. And this would be seven thousand six hundred and fifty right over here.

And so, 7652 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 hundred for nine hundred and eighty-two. What would that be? Well, once again, we look at the hundreds place.

Well, what's a hundred that's right below 982? Well, if you just get rid of the 82, you're just left with nine hundreds, so that would be 900 if you round down. And if you were to round up, what's the hundreds right above this? Well, you could go from nine hundreds to ten hundreds, and that would be the same thing as one thousand.

And so, I wanted to show this example because when you're rounding up here, the next hundred is ten hundreds or one thousand. And so, we can see very clearly here that if we look at the tens place, the eight is greater than or equal to five, so we are going to round up.

So, 982 rounded to the nearest hundreds is one thousand.