Rounding to the Nearest 1,000, 10,000 & 100,000 | Using Number Lines

Welcome to Math with Mr. J. In this video I'm going to cover how to round to the nearest thousand, ten thousand, and hundred thousand using number lines. Using number lines here is going to give us a nice visual of rounding and help our overall understanding of rounding. We'll start with rounding to the nearest thousand and then go from there. Everything is time stamped and put into chapters so feel free to jump around to different examples. Let's jump into number one where we have four thousand three hundred eighty two. We need to round this to the nearest thousand. Now the first thing we need to do here is find our end points. Since we are rounding to the nearest thousand we need to find the two multiples of one thousand that four thousand three hundred eighty two is between. So one thousand, two thousand, three thousand, four thousand, and so on. Which two thousands is four thousand three hundred eighty two between? Well we know four thousand three hundred eighty two is between four thousand and five thousand. It's greater than four thousand and less than five thousand. Let's mark those on our number line here. So four thousand and five thousand. Again we can call these our end points and our number here four thousand three hundred eighty two is either going to round to four thousand or five thousand when we round to the nearest thousand. Now we need to find the mid point which is the halfway point between four thousand and five thousand. That's going to be four thousand five hundred and that's right in the middle here. That midpoint is really important. It's going to help us round. It's going to help us figure out the nearest thousand. Now we need to plot our number on our number line four thousand three hundred eighty two is between four thousand and four thousand five hundred. It's greater than four thousand and less than that midpoint of four thousand five hundred. It's going to be right around here so we can put four thousand three hundred eighty two. Lastly we round. So is four thousand three hundred eighty two closer to four thousand or five thousand? Well let's use our midpoint. Anything to the left of the midpoint rounds down to four thousand. Anything to the right of the midpoint rounds up to five thousand. And keep in mind if a number is exactly at the midpoint it always rounds up as well. Four thousand three hundred eighty two is to the left of four thousand five hundred to the left of the midpoint. That means it's closer to four thousand than it is to five thousand. Four thousand three hundred eighty two rounds to four thousand when rounded to the nearest thousand. 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. Four thousand three hundred eighty two is not equal to four thousand 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 seven thousand eight hundred forty five. First let's figure out our end point which two thousand seven thousand eight hundred forty five is between. That's going to be seven thousand and eight thousand. So seven thousand and eight thousand. Now we need the midpoint which is going to be seven thousand five hundred. So right here in the middle. Next we plot our number on the number line. Seven thousand eight hundred forty five is between seven thousand five hundred and eight thousand. It's greater than the midpoint but less than eight thousand. Seven thousand eight hundred forty five is right around here. So seven thousand eight hundred forty five. Now let's round. Which thousand is our number closer to? We are to the right of the midpoint. Seven thousand eight hundred forty five is closer to eight thousand than it is to seven thousand. So seven thousand eight hundred forty five rounds to eight thousand when rounded to the nearest thousand. Moving on to number three we have twenty five thousand six hundred four. Let's round to the nearest thousand. Now for this one we have a number that goes to the ten thousands place. So we don't just want to use twenty thousand and thirty thousand for our end points. These would be correct if we were rounding to the nearest ten thousand. But we're not. We're rounding to the nearest thousand. So this is incorrect. Let's clear this. We need to round to the nearest thousand here. So we want the thousand that comes before and the thousand that comes after twenty five thousand six hundred four. Think about counting by thousands. So twenty five thousand twenty six thousand twenty seven thousand and so on. Twenty five thousand six hundred four is between twenty five thousand and twenty six thousand. So our end points here. Twenty five thousand and twenty six thousand. Now we need our midpoint. That's going to be twenty five thousand five hundred. And now we plot our number on the number line. Our number is just to the right of the midpoint here. Twenty five thousand six hundred four is going to be right around here. So twenty five thousand six hundred four. So that's greater than twenty five thousand five hundred and less than twenty six thousand. So is twenty five thousand six hundred four closer to twenty five thousand or twenty six thousand? Well, this is just to the right of the midpoint, so it's closer to twenty six thousand. Twenty five thousand six hundred four rounds to twenty six thousand when rounded to the nearest thousand. Lastly, moving on to number four, we have sixty two thousand one hundred ninety three. Let's round to the nearest thousand. There's a two in the thousands place here. So we need to think which two thousands this is between. Sixty two thousand one hundred ninety three is between sixty two thousand and sixty three thousand. So those are our end points here. So again, this is between sixty two thousand and sixty three thousand. Then our midpoint is going to be sixty two thousand five hundred. Now, sixty two thousand one hundred ninety three is greater than sixty two thousand and less than our midpoint of sixty two thousand five hundred. It's going to be right around here. So sixty two thousand one hundred ninety three. And we can see that sixty two thousand one hundred ninety three is to the left of the midpoint and closer to sixty two thousand. Sixty two thousand one hundred ninety three rounds to sixty two thousand when rounded to the nearest thousand. Now let's move on to rounding to the nearest ten thousand. Here's our section on rounding to the nearest ten thousand. Let's jump into number one where we have forty six thousand seven hundred fifty five. Let's round to the nearest ten thousand. Now, the first thing that we need to do here is find our end points. Since we are rounding to the nearest ten thousand, that means we need to find the two multiples of ten thousand that our number is between. So ten thousand, twenty thousand, thirty thousand, forty thousand and so on. Which two ten thousands is forty six thousand seven hundred fifty five between? Well, we know that forty six thousand seven hundred fifty five is between forty thousand and fifty thousand. It's greater than forty thousand and less than fifty thousand. Let's mark those on our number line. So these are our end points here. Forty thousand and fifty thousand. Now our number is going to round to one of these end points. This will either round to forty thousand or fifty thousand. Now we need the midpoint, which is the halfway point between forty thousand and fifty thousand. That's going to be forty five thousand. So right here in the middle. Now we plot our number on our number line. Forty six thousand seven hundred fifty five is greater than forty five thousand and less than fifty thousand. So it's going to be right around here. So forty six thousand seven hundred fifty five. Lastly, we need to round. So is forty six thousand seven hundred fifty five closer to forty thousand or fifty thousand? Well, let's use our midpoint to help us round. Forty six thousand seven hundred fifty five is to the right of our midpoint here. It's closer to fifty thousand than it is to forty thousand. So forty six thousand seven hundred fifty five rounds to fifty thousand when rounded to the nearest ten thousand. Moving on to number two, we have eighty one thousand two hundred sixty. First, let's figure out our end points. Which two ten thousands is our number between? Well, eighty thousand and ninety thousand. So let's mark those on our number line. So eighty thousand and ninety thousand. Now we need the midpoint and we'll use that midpoint to help us round. The midpoint here is going to be eighty five thousand. Eighty one thousand two hundred sixty is greater than eighty thousand, but less than that midpoint of eighty five thousand. It's going to be right around here. So eighty one thousand two hundred sixty. So is our number here closer to eighty thousand or ninety thousand? Well, it's to the left of the midpoint and we can see that it's closer to eighty thousand. So eighty one thousand two hundred sixty rounds to eighty thousand when rounded to the nearest ten thousand. Moving on to number three, we have five hundred thirty four thousand two hundred eighty two. Let's round to the nearest ten thousand. Now for this one, we have a number that goes to the hundred thousands place. So don't automatically use five hundred thousand and six hundred thousand for our end points. Those would be correct if we were rounding to the nearest hundred thousand, but we're not. We're rounding to the nearest ten thousand. So five hundred thousand and six hundred thousand are incorrect for this. We want the ten thousand that comes before and the ten thousand that comes after five hundred thirty four thousand two hundred eighty two. Think about counting by ten thousands here. So five hundred ten thousand, five hundred twenty thousand, five hundred thirty thousand, five hundred forty thousand and so on. We need to focus on the ten thousands place here where we have a three representing thirty thousand. We can even include the four in the thousands place and think about thirty four thousand. This is between five hundred thirty thousand and five hundred forty thousand. Those are our end points. So let's mark those. We have five hundred thirty thousand and five hundred forty thousand. Now our midpoint is going to be five hundred thirty five thousand. Our number five hundred thirty four thousand two hundred eighty two is a little less than that midpoint. It's right around here. So five hundred thirty four thousand two hundred eighty two. So is our number closer to five hundred thirty thousand or five hundred forty thousand? Well it's to the left of the midpoint so it's closer to five hundred thirty thousand. Five hundred thirty four thousand two hundred eighty two rounds to five hundred thirty thousand when rounded to the nearest ten thousand. Lastly let's move on to number four where we need to round two hundred seventy eight thousand six hundred thirty nine to the nearest ten thousand. Think about our end points here. The two ten thousand our number is between. We have a seven in the ten thousands place representing seventy thousand. And if we include the eight in the thousands place we can look at this as seventy eight thousand. So our end points are going to be two hundred seventy thousand and two hundred eighty thousand. So let's mark these here. We have two hundred seventy thousand and two hundred eighty thousand. Then our midpoint is going to be two hundred seventy five thousand. Now let's plot our number which is greater than the midpoint. It's right around here. So two hundred seventy eight thousand six hundred thirty nine. So two hundred seventy eight thousand six hundred thirty nine rounds to two hundred eighty thousand when rounded to the nearest ten thousand. Now let's move on to rounding to the nearest hundred thousand. Here's our section on rounding to the nearest hundred thousand. Let's jump into number one where we need to round three hundred sixty four thousand two hundred eighty to the nearest hundred thousand. Now the first thing that we need to do here is find our end points. Since we are rounding to the nearest hundred thousand we need to find the two multiples of one hundred thousand that our number is between. So one hundred thousand two hundred thousand three hundred thousand four hundred thousand and so on. Which two hundred thousand is three hundred sixty four thousand two hundred eighty between. Well we know this is between three hundred thousand and four hundred thousand. Three hundred sixty four thousand two hundred eighty is greater than three hundred thousand and less than four hundred thousand. So again we can call these our end points. Let's mark them on our number line here. So 300,000 and 400,000. Our number is going to round to one of these end points. This will either round to 300,000 or 400,000. Now we need the midpoint, which is the halfway point between 300,000 and 400,000. That's going to be 350,000. So right here in the middle. Now let's plot our number on our number line. 364,280 is between 350,000, our midpoint, and 400,000. It's going to be right around here. So 364,280. Lastly, we need to round. So is our number closer to 300,000 or 400,000? Well, let's use our midpoint. Our number here is to the right of the midpoint. So 364,280 rounds to 400,000 when we round to the nearest 100,000. Moving on to number two, we have 628,946. Let's round to the nearest 100,000. First, let's figure out our end points. Which 200,000 is our number between? Well, 600,000 and 700,000. Those are our end points here. So let's mark those. We have 600,000 and 700,000. Now we need our midpoint. That's going to be 650,000. 628,946 is greater than 600,000 and less than the midpoint of 650,000. It's going to be right around here. So 628,946. So which 100,000 are we closer to here? 600,000 or 700,000? Well, we're to the left of the midpoint and closer to 600,000. So 628,946 rounds to 600,000 when rounded to the nearest 100,000. Moving on to number three, we have 149,328. Let's round to the nearest 100,000. So what are our end points here? Which 200,000 is this between? Well, 100,000 and 200,000. So 100,000 and 200,000. Our midpoint here is 150,000. Now let's plot our number. 149,328 is close to our midpoint here, but slightly less, slightly to the left. So right about here. So 149,328. Now again, this is close to the midpoint, but it's slightly to the left. That tells us our number is closer to 100,000. So 149,328 rounds to 100,000 when rounding to the nearest 100,000. Lastly, let's move on to number four, where we need to round 984,550 to the nearest 100,000. And this one is a little interesting. Let's start with the end points. Which 200,000 is this between? Well, our number is greater than 900,000. So that's our first end point. But what's our other end point? Think about counting up by 100,000. What comes next after 900,000? 1,000,000. So 1,000,000 is our other end point here. 1,000,000 is a multiple of 100,000. So this does work for one of our end points. Now our midpoint is 950,000. So let's mark that. And now we can plot our number. 984,550 is greater than that midpoint. It's right around here. So 984,550. So our number is to the right of the midpoint and closer to 1,000,000. 984,550 rounds to 1,000,000 when rounded to the nearest 100,000. So there you have it. There's how to round to the nearest 1,000, 10,000 and 100,000 using number lines. I hope that helped. Thanks so much for watching. Until next time, peace.