Lesson Video: Rounding to the Nearest Thousand Mathematics

In this video, we will learn how to round whole numbers within 10,000 to the nearest thousand by identifying the hundreds numbers it is between on a number line.

17:55

Video Transcript

Rounding to the Nearest Thousand

In this video, we’re going to learn how to round whole numbers to the nearest thousand. We’re going to do this by spotting the thousands numbers it’s between on a number line and also using place value to help.

Welcome to Chickenville, population 2,295. The number of chickens that live in this town is a four-digit number. But what if we just want a rough idea of the population without knowing the exact number? A word we sometimes used in maths is approximately. It’s a word that we use to describe a number, maybe a measurement, that is around about the exact number. It’s not exact, but it’s close enough to be used. So approximately, how many chickens live in this town? In this video, we’re going to be rounding numbers. When we round a number, we make it simpler while still keeping its value close to what it was. We could make the population of Chickenville simpler by rounding to the nearest ten, maybe the nearest hundred. But in this video, we’re going to be looking at rounding to the nearest thousand.

Now what do we know about the number 2,295? Well, we can work out the two 1000s number that it’s between. This is going to be helpful to us because we’re either going to need to round it up or down. Let’s sketch a number line to help us. The number that we’re thinking of is made up of two 1000s, two 100s, nine 10s, and five ones. And to work out which two multiples of a thousand that this number comes in between, we can look at the thousands digit to help us. It’s a two. Our number is two thousand something. This digit tells us that our number comes after 2,000 but before 3,000.

But which of these thousands numbers is it nearest to? Should we round it up to 3,000? Or what about down to 2,000? Let’s split our number line into 10 intervals. There we are. Each interval is worth 100. Now where we’re using a number line like this to round a number, it’s always useful to find the midway point. It’s five intervals along here. And what’s halfway between 2,000 and 3,000? It’s 2,500. And knowing this midway point can help us decide whether to round up or down. If our number is more than 2,500 and belongs somewhere here on the number line, we can round it up because it’s nearest to 3,000. And hopefully, you might remember from previous work on rounding; this also applies to the halfway point too. If our number was 2,500 itself, we’d also round it up. But then, if our number is less than this midway point, we’re going to need to round down. It’s going to be nearest to 2,000.

Let’s plot where our number belongs on this number line and we’ll see which side of the midway point it falls. To help us do this, we now need to look at the hundreds digit. It’s a two. Our number is two thousand two hundred something. Well, we know that 2,200 is two intervals along our number line. But because the tens and the ones in our number are 95, it’s very close to 2,300. So maybe we’d better mark it around about here. Hopefully, we can see two things now. Firstly, this number is less than 2500. But also, clearly the nearest thousands number is 2,000. We need to round this number down. 2,295 when rounded to the nearest thousand is 2,000.

By the way, look at the words in orange that you can see on the screen. These are the sorts of words we use when we’re talking about numbers that have been rounded. There’s about 2,000 chickens in Chickenville. There are approximately or roughly 2,000 chickens in Chickenville. And in this video, we’re going to try to use words like this when we can to show that we’re not dealing with an exact number but a rounded one, a number that we’ve made simpler, but we’ve kept its value quite close to what it was.

Now, in this example, we used a number line to help us. But there is another method we could use to help us round numbers to the nearest thousand, and that’s by using our knowledge of place value to help. Let’s show this using another example. Let’s imagine that we were just passing through Chickenville. About how far is it to the next town? We can see from the sign that Roostertown is 4,516 meters away. This is just over four kilometers. Now, as we’ve said already, we could round this number to the nearest ten or the nearest hundred. But in this video, we’re rounding to the nearest thousand so we’d better do that. And we need to think about the place value of all the digits in 4,516. Let’s use a place value group to help.

4,516 is made up of four 1000s, five 100s, one 10, and six ones. Now, which place value column do we need to look at when we want to round to the nearest 1000? Well, there are two really. The hundreds column is going to tell us whether to round up or down, so this one’s pretty important. But it’s also important to look at our thousands column to know what we’re rounding up or down to. Let’s start with the thousands digit. 4,516 has a four in the thousands place. Now to find a multiple of thousand that is less than this number, in other words, the number that we would round down to if we wanted to, we just need to take this thousands digit and forget about the others for a moment. This gives us the number 4,000.

And, of course, to find the next multiple of a thousand after our number, we just need to alter the thousands digit. So because it’s a four, we need to change it into a five. So just by looking at our thousands digit, we can tell that we’re either going to round it down to 4,000 or up to 5,000. And whether we round up or down is decided by the digit in the hundreds place. Perhaps you can remember the rule that we used to help us here. If the digit is five or more, so that’s five, six, seven, eight, or nine, we round up. And if the digit is four or less, so that’s four, three, two, one, and also in this example zero, we round down. In this example, 4,516, we have the digit five in the hundreds place.

In a way, this is a useful digit to look at because five is halfway. But you might think, “Oh, but we’ve got one 10 and six ones, so this is more than halfway.” But you know, even if our tens and our ones were zeros and this number was exactly halfway between 4,000 and 5,000, we’d still know what to do because if our number has the digit five or more in the hundreds place, we round up. 4,516 rounded to the nearest 1,000 is 5,000. And so, we could say that the next town is approximately 5,000 meters away.

Now you could look at the distance on the sign and think, “Well, it’s not that close to 5,000 meters. It’s a bit of a strange answer to give if we’re asking how far it is to the next town.” But remember, this video is all about rounding to the nearest thousand. And so really, we can think of our question as asking, how far is it to the next town to the nearest thousand meters?

Right, so we got all the tools now that we need to round numbers to the nearest thousand. So, let’s put them into practice. Let’s answer some questions, and we’re going to use both number lines and also our knowledge of place value to help.

Round 7,412 to the nearest thousand.

This question gives us a four-digit number 7,412, and we’re told to round it. Do you remember what rounding a number means? This is when we make a number simpler whilst keeping it near to its exact value. So, we might round a number to its nearest ten or nearest hundred. These are simpler ways of writing numbers. But in this question, we need to round our number to the nearest thousand. In other words, our answer is going to have three zeros at the end of it. And you know, we can be so sure of this we could draw an answer box before we even start and put those three zeros ready. But how many thousands is 7,412 nearest to?

We could use a number line to help us find out. First of all, we need to think of the two multiples of a thousand that our number is in between. We know that 7,412 comes after 7,000 but before 8,000. So it comes somewhere in between. It’s somewhere on our number line, but whereabout? We could divide our number line into 10 intervals and, first of all, mark the midway point. This is here. And we know that the halfway point between 7,000 and 8,000 is 7,500. And labeling this midway point can help us to see whether to round our number up or down. Because if our number is 7,500 itself or any number larger than this, we need to round it up to 8,000. And if our number is on the other side of our midway point, in other words, if it’s less than 7,500, we need to round it down to 7,000. So, the big question is, is 7,412 less than or greater than 7,500?

Well, if we look at the digit in the hundreds place, we can see that it’s a four. If each of the intervals on our number line is worth 100, then we’d plot 7,412 maybe about here, just after the fourth notch. Now, we can see straightaway which multiple of a thousand it’s nearest to. It’s to the left of our halfway point as we need to round it down to 7,000. And by rounding our number like this, we’ve made the number simpler, whilst keeping it near to its exact value. 7,412 rounded to the nearest thousand is 7,000.

Benjamin has 6,624 dollars. He wants to round this number to the nearest thousand. Complete. The number 6,624 is between what and what. 4,000 and 5,000; 5,000 and 6,000; 6,000 and 7,000; or 7,000 and 8,000. How much money to the nearest thousand does Benjamin have?

In this question, we’re told that Benjamin has a four-figure sum of money. He has 6,624 dollars. And we’re also told that he wants to round this number to the nearest thousand. When we round a number, we make it simpler. Perhaps Benjamin has been asked about, how much money do you have? Or maybe, can you tell me roughly how much you have? And so, he doesn’t need to say the exact amount he can make the number simpler. He can round it to the nearest thousand.

And the first thing he needs to do is to think about the two multiples of a thousand that this number is in between. Then, he knows, whether he rounds it up or down, what numbers he’s rounding to. And the first part of this question takes us through this. We’ve got a sentence that we need to complete. The number 6,624 is between what and what. Let’s think about this number for a second. It’s made up of six 1000s, six 100s, two 10s, and four ones. Now, which of these digits do you think is most important if we’re thinking about the multiples of a thousand that this number is in between? It’s the thousands digit. It tells us where this number belongs.

Benjamin’s number has a six in the thousands place. It’s six thousand something, so it’s greater than 6,000. But if Benjamin carried on counting from his number, the next 1,000 after his number would be 7,000. The number 6,624 is between 6,000 and 7,000. Now, which one of these is Benjamin going to round his number to? Is he going to round it down or up? The last part of the question asked us to actually find the answer. How much money to the nearest thousand does Benjamin have?

We can find the answer by looking at a different digit. This time, we can look at the hundreds digit, which is a six. And we can remember one of the rules about rounding here. If the digit is a five or more, so that’s five, six, seven, eight, or nine, we round our number up. And our hundreds digit is a five or more, so we need to round our number up. So, when Benjamin is asked the question, “About how much money do you have?”, he can say, well, roughly 7,000 dollars. In this question, we rounded an amount of money to the nearest thousand. By looking at the thousands digit, we could tell that the number 6,624 is between 6,000 and 7,000. And then by looking at the hundreds digit, we knew we had to round up. Benjamin has to the nearest thousand dollars 7,000 dollars.

What is 862 to the nearest thousand?

In this question, we’re given a three-digit number 862 and we need to write it to the nearest thousand. In other words, we need to round it. But wait a moment. Our number only contains three digits. This means it has a number of hundreds, tens, and ones, but there aren’t any thousands. Normally, when rounding a number to the nearest thousand, we go straight to the thousands digit. We’d use this to help us see which thousands the number is in between. So, what do we do if we don’t have any thousands? Well, really, we do exactly the same as if there were some thousands. Firstly, we take the thousands digit, which we can say here is a zero. There’s nothing there, is there? And we ignore all the other columns. Now, if we were to do that, we just have zero. So let’s write that down. The multiple of 1,000 less than 862 is actually zero.

Now, you might think, how is zero a multiple of 1,000? Well, a multiple of 1,000 is what we get when we multiply any number by 1,000. And we get zero if we multiply zero by 1,000. Now, do you remember how to find the multiple of 1,000 greater than this one? We just increase our number of thousands by one, which is 1,000. So, we know our number comes between zero and 1,000. But what is the nearest multiple of 1,000? Are we going to round down or up? We can look at the hundreds digit to help us. Thankfully, we do have a digit in the hundreds place, and it’s an eight. We know that if a digit is four or less, we round down. But if it’s worth five or more, in this case it is, we round up. And so, we can round this three-digit number to the nearest thousand. 862 to the nearest thousand is 1,000.

So, what have we learned in this video? We have learned how to round whole numbers to the nearest thousand using number lines and place value to help.

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