How to Round to the Nearest 10,000 Using a Number Line | Lesson + Practice

Welcome to Math with Mr. J. In this video, I'm going to cover how to round to the nearest 10,000, and we're going to be using number lines to help us round. Number lines are going to give us a nice visual of rounding, and they'll help our overall understanding. We'll go through some examples together, and then I'll give you some practice problems that you can try on your own. Let's jump into number one, where we have 46,755. Let's round to the nearest 10,000. Now, the first thing that we need to do here is find our end point. Since we are rounding to the nearest 10,000, that means we need to find the two multiples of 10,000 that our number is between. So 10,000, 20,000, 30,000, 40,000, and so on. Which two 10,000s is 46,755 between? Well, we know that 46,755 is between 40,000 and 50,000. It's greater than 40,000 and less than 50,000. Let's mark those on our number line. So these are our end points here, 40,000 and 50,000. Now, our number is going to round to one of these end points. This will either round to 40,000 or 50,000. Now, we need the midpoint, which is the halfway point between 40,000 and 50,000. That's going to be 45,000, so right here in the middle. That midpoint is really important. It's going to help us round. It's going to help us figure out the nearest 10,000. Now, we plot our number on our number line. 46,755 is greater than 45,000 and less than 50,000. So it's going to be right around here. So 46,755. Lastly, we need to round. So is 46,755 closer to 40,000 or 50,000? Well, let's use our midpoint to help us round. Anything to the left of the midpoint rounds down to 40,000. Anything to the right of the midpoint rounds up to 50,000. And keep in mind, if a number is exactly at the midpoint, it also rounds up. 46,755 is to the right of our midpoint here. It's closer to 50,000 than it is to 40,000. So 46,755 rounds to 50,000 when rounded to the nearest 10,000. By the way, that squiggly equal sign is the approximate symbol. And we can use it when rounding. This tells us we have a number that's close but not exact. 46,755 is not equal to 50,000. So we can't use an equal sign. Instead, we use the approximate symbol to show that we rounded. Moving on to number two, we have 81,260. First, let's figure out our end points. Which two 10,000s is our number between? Well, 80,000 and 90,000. So let's mark those on our number line. So 80,000 and 90,000. Now we need the midpoint. And we'll use that midpoint to help us round. The midpoint here is going to be 85,000. 81,260 is greater than 80,000 but less than that midpoint of 85,000. It's going to be right around here. So 81,260. So is our number here closer to 80,000 or 90,000? Well, it's to the left of the midpoint. And we can see that it's closer to 80,000. So 81,260 rounds to 80,000 when rounded to the nearest 10,000. Moving on to number three, we have 534,282. Let's round to the nearest 10,000. Now for this one, we have a number that goes to the 100,000 place. So don't automatically use 500,000 and 600,000 for our end points. Those would be correct if we were rounding to the nearest 100,000. But we're not. We're rounding to the nearest 10,000. So 500,000 and 600,000 are incorrect for this. We want the 10,000 that comes before and the 10,000 that comes after 534,282. Think about counting by 10,000s here. So 510,000, 520,000, 530,000, 540,000, and so on. We need to focus on the 10,000s place here where we have a 3 representing 30,000. We can even include the 4 in the thousands place and think about 34,000. This is between 530,000 and 540,000. Those are our end points. So let's mark those. We have 530,000 and 540,000. Now our midpoint is going to be 535,000. Our number 534,282 is a little less than that midpoint. It's right around here. So 534,282. So is our number closer to 530,000 or 540,000? Well, it's to the left of the midpoint. So it's closer to 530,000. 534,282 rounds to 530,000 when rounded to the nearest 10,000. Lastly, let's move on to number 4 where we need to round 278,639 to the nearest 10,000. Think about our end points here. The two 10,000s, our number is between. We have a 7 in the 10,000s place representing 70,000. And if we include the 8 in the 1,000s place, we can look at this as 78,000. So our end points are going to be 270,000 and 280,000. So let's mark these here. We have 270,000 and 280,000. Then our midpoint is going to be 275,000. Now let's plot our number which is greater than the midpoint. It's right around here. So 278,639. So 278,639 rounds to 280,000 when rounded to the nearest 10,000. Now that we've gone through some examples together, it's time for you to try some practice problems on your own. So have paper and a pencil ready. So here are your practice problems. I'll give you five minutes and then we will go over the answers. Feel free to pause if you need more time or jump ahead to the answers whenever you are ready. Go ahead and start. Okay, so that was five minutes. Let's go over the answers. So here are our answers. Remember, we're rounding to the nearest 10,000 here. For number one, we should have 40,000. For number two, 70,000. For number three, 30,000. For number four, 650,000. For number five, 120,000. And then lastly, for number six, 950,000. Feel free to pause at this point if you need more time to check your work. So there you have it. There's how to round to the nearest 10,000 using number lines. I hope that helped. Thanks so much for watching. Until next time, peace.