Rounding to nearest 100

We're asked to round 152, 137, 245, and 354 to the nearest 100, which is another way of saying round each of these numbers to the nearest multiple of 100. So let's think about them one by one. So let's draw a number line here. And here I'm counting up by hundreds. What I've marked here, 100, 200, 300, 400, these are all multiples of 100. I could keep going up. I could go to 500, 600, so on and so forth. Now, let's start with 152. Well, where does 152 sit? So halfway in between is 150. 152 is going to be right to the right of that. So that's 152 right over here. So what are our two options? We might round up. The multiple of 100 above 152 is 200. The multiple of 100 below 152 is 100. So which direction do we go in? Do we round up to 200, or do we round down to 100? Well, if we're rounding to the nearest 100, we want to look at one place to the right of that. We want to look at the tens place to decide which multiple of 100 it is closer to. And the rules are very similar to when we're rounding to the nearest tens place or really any place. We look one place to the right of it. So in this case, we look at the tens place. And we say, if this is 5 or larger, we round up. And this is 5 or larger, so we're going to round up to 200. So this we're going to round. 152, we're going to round to 200, which also makes sense. 152 is a little bit closer to 200. It's 48 away from to 200 than it to 100. It's 52 away from 100. So it makes sense to go up to the nearest multiple of 100. Now, let's think about 137. And I encourage you to now pause the video and try to round each of these other three numbers to the nearest 100. Well, 137 is going to sit someplace right over here. 137 is going to be right over there. So two options-- we can round down to 100. That's the multiple of 100 below 137. Or we could round up to 200. Well, 137, just looking at it, is clearly closer to 100. Or we could apply our rule. If we're rounding to the nearest 100, we want to look at one place to the right of that. We want to look at the tens place. If this is 5 or larger, we round up. If it's less than 5, we round down. So in this case, we would round down to 100. Let's do the same thing with 245. If you haven't paused it and tried it yourself, once again, I want to emphasize. That'll make it really valuable for you to try it on your own. So let's plot where 245 is. So 245 is right around-- this is 250, so 245 might be right around here. Now, let's apply that rule. If we're trying to round to the nearest 100, we would look to one place to the right. We'll look at the tens place. We could ignore the ones place. We look at the tens place here. If it is greater than or equal to 5, we round up. If it is less than 5, we round down. So here, we're clearly going to round down. And when we round down, we're going to round down to the multiple of 100 that's directly below 245. Well, we're going to round down to 200. We had two options. If we rounded up, we would have gone to 300. If we rounded down, we would go to 200. We're clearly closer to 200. And we can verify that with the rule. The tens place, we're in the 40's here. The tens place is a 4. We're going to round down. Now let's think about 354. If we were to plot that, this is 350. 354 might be right over here. So if we rounded down, we would go to 300. If we rounded up, we would go to 400. Now let's apply our rule, and let's also think about it on the number line. This is all about finding the multiple of 100 that it's closest to. If you're trying to round to the nearest 100, you want to look at the tens place, a place to the right of the place you're rounding to. If the tens place is a 5 or larger, you're going to round up. This is a 5 or larger so we're going to round up to 400. And that also makes sense. The rule is really valuable. If you're right at 350, right in between, then you would need the rule to say, hey, let's look at this 5 and round up. But 354 is also closer to 400 than it is to 300. It's 54 away from 300. It's 46 away from 400. So it makes sense that we would round up to 400.