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Lesson Video: Rounding Numbers up to 100,000 Mathematics

In this video, we will learn how to round whole numbers within 100,000 to any place value using number lines and by considering the value of each digit.

16:23

Video Transcript

Rounding Numbers up to One Hundred Thousand

In this video, we’re going to learn how to round whole numbers within one hundred thousand to any place value. We’re going to do this using number lines and also by thinking carefully about the value of each digit.

Let’s start by imagining a farm that’s a lot larger than your average farm. The number of sheep on this farm is a massive 14,796. Now, every month the farmers get together and have a chat about the size of each flock. And when this particular farmer describes how many sheep he has, he doesn’t give the exact figure. No one really wants to know the exact figure. Instead, he rounds it.

As I’m sure you know, rounding a number is a way to say it more simply. We say it to the nearest ten or hundred or thousand and so on. Because this is a five-digit number, there are four possible ways we could round it. We can’t round it to the nearest one; that doesn’t make sense. But we could round it to the nearest ten, hundred, thousand, or even to the nearest ten thousand.

Let’s start by thinking about what this number would be if we rounded it to the nearest ten. Now, there are going to be two digits that are important to us here. One is the tens digit. This is going to give us an idea of where the number belongs. But then also the digit to the right of this is important. This is going to tell us whether to round the number up or down.

The tens digit of 1,796 is a nine. This digit shows us that our five-digit number comes somewhere between 14,790 and the next multiple of ten after this, which is 14,800. But which of these two multiples of ten is our number nearest to? Should we round it up or down?

We’re using a number line to help us here. And one of the important things that we can do when using a number line is to mark the midway point. Then it can help us place our number. And halfway between 14,790 and 14,800 is 14,795. Now that we’ve marked this halfway point, we can see which side of it our number belongs. And what’s going to help us here is the digit to the right of the tens place. Our number 14,796 is greater than 14,795. If we were to estimate its position on this number line, perhaps it would be about here. And because it’s greater than the midway point, we can round it up. The number of sheep on our farm, rounded to the nearest ten, is 14,800.

Hopefully, you can see that if our farmer was talking to his friends, it’s much simpler to be able to say, “Oh, I’ve got about 14,800 sheep.” It’s a much simpler number. And I’m sure you’ve practiced rounding two-, three-, and four-digit numbers before. But now that we’re rounding five-digit numbers, we’ve got a new column to think about.

What if our farmer wants to describe the number of sheep even more simply? What if he rounds it to the nearest ten thousand? This is our new column with five-digit numbers. But it’s just as straightforward to round to the nearest ten thousand as it is to round to the nearest ten. Again, we really just need to think about two columns. The ten thousands digit is going to give us an idea of where our number belongs. And then the digit to the right of this, which is the thousands digit, is going to tell us whether to round it up or down.

So to begin with, the ten thousands digit is a one. This tells us that the two multiples of ten thousand that our number’s between are 10,000 and 20,000. And once again, if we mark the halfway point, it’s going to help us. Halfway between 10,000 and 20,000 is of course 15,000. But where does our number belong?

It’s time to look at the digit to the right. Our number is 14,796. And so the thousands digit is a four. 14,000 is less than 15,000. So perhaps we’d put it about here on the number line. And because it’s less than 15,000, we’re going to need to round it down. The number of sheep rounded to the nearest ten thousand is actually 10,000. Depending on whether our farmer rounds his sheep to the nearest ten, hundred, thousand, or ten thousand, he’s gonna get a different answer. Just look at the difference between these two numbers. If he rounds his total to the nearest ten thousand, it’s gonna sound a lot less than if he rounds it to the nearest ten. Doesn’t always work like this. But in this particular number, the digits meant that we had to round down. It’s made a big difference.

Let’s try answering a couple of questions now where we can use number lines to help us round some five-digit numbers.

Look at the given number line. If we round 14,189 to the nearest ten thousand, what do we get? If we round 14,189 to the nearest thousand, what do we get? And if we round 14,189 to the nearest hundred, what do we get?

Let’s start by doing what the first sentence tells us to do, having a good look at the number line we’re given. We can see that on either end of this number line, there’s a multiple of 10,000. We’ve got 10,000 at one end and 20,000 at the other. And there are 10 jumps or intervals just like this one in between. So each interval must be worth another 1,000. After 10,000, we have 11,000, 12,000, 13,000, and so on, all the way up to 20,000. The last thing to notice about our number line is this speech bubble here. Inside it, we’ve got a five-digit number. And it’s this five-digit number that our three questions are based on.

Firstly, we’re asked, if we round 14,189, which is the number in the speech bubble, to the nearest ten thousand, what do we get? Well, this number line is perfect for answering this question. The nearest ten thousand is either going to be 10,000 or 20,000. As well as thinking about the two numbers at either end, it’s also important when using a number line to think about the halfway point. And halfway between 10,000 and 20,000 is 15,000. And because 14,189 is about here on our number line, we can see that it’s less than 15,000. The nearest multiple of 10,000 is 10,000 itself. We’re going to need to round this number down. 14,189 rounded to the nearest ten thousand is 10,000.

Next, we’re asked to round the same number, but this time to the nearest thousand. Now, do you remember we said that each interval on our number line was worth 1,000 more? So to find the answer to this second question, we really just need to zoom in and think about part of our number line, this part here. Let’s sketch a new number line to show what we mean.

Now, we know from looking at our first number line that the two multiples of a thousand that our number’s in between are 14,000 and 15,000. And one of these is going to be our answer. But before we start to think about whether to round our number up or down, let’s mark that halfway point again. Halfway between 14,000 and 15,000 is 14,500. If we look at the hundreds digit in our number, it’s a one. So where would we estimate it belongs on our number line? Maybe somewhere like here? We know that fourteen thousand one hundred and something is less than 14,500. So once again, we’re going to have to round our number down. 14,189 rounded to the nearest thousand is 14,000.

Finally then, we need to round our number one more time, this time to the nearest hundred. If we split our previous number line into 10 intervals just like before, each one would be worth 100. And the part of this number line that we need to use to find the answer to this last question is this part here. Let’s zoom in to it. As we’ve said already, the hundreds digit in 14,189 is a one. This tells us that the two multiples of a hundred that our number’s in between are 14,100 and 14,200. One of these is going to be our answer. Let’s mark the halfway point again. Halfway between 14,100 and 14,200 is 14,150.

Now, to help us work out whether to round our number up or down, we need to look at the digit to the right of the hundreds digit. The tens digit in our number is an eight. Fourteen thousand one hundred and eighty something is larger than 14,150. It’s probably about here on our number line. This time, we’re going to need to round up.

In this question then, we had a go at taking the same number but rounding it in different ways. And we thought about how number lines can help us. If we round 14,189 to the nearest ten thousand, we get the answer 10,000. If we round the same number to the nearest thousand, we get 14,000. And if we round it to the nearest hundred, we get the answer 14,200.

Round 80,531 to the nearest thousand.

We could use a number line to help us solve this problem. For us to be able to round 80,531 to the nearest thousand, we need to know what the two multiples of a thousand either side of this number are. To help us, we can start by looking at the thousands digit itself. In this number, it’s a zero. This tells us that our number comes somewhere between 80,000 and 81,000. One of these numbers is going to be our answer, but which one?

Before we continue, let’s mark the halfway point on our number line. Halfway is 80,500. Now, to work out where our number belongs on this number line and whether to round it up or down, we need to look at the digit to the right of the thousands digit. The hundreds digit is a five. Our number is eighty thousand five hundred and something. This means we could say it’s about here on our number line, just past halfway. We can see we’re going to need to round it up to the nearest thousand. 80,531 rounded to the nearest thousand is 81,000.

So far, we’ve used number lines to help us. But do we have to sketch a number line every single time that we want to round something? Not at all. We can use what we know about place value instead. Let’s see how.

What is the smallest whole number that when rounded to the nearest hundred gives a result of 95,200?

Often when we’re asked a question about rounding numbers, we’re given a number and asked to round it up. But in this question, we need to think backwards. We’re given the answer, the rounded number, but we need to find the smallest whole number that will round to this number when we round it to the nearest hundred.

To begin with then, let’s think about the rounded number that we have. 95,200 is made up of nine lots of 10,000, five 1,000s, and two 100s. Now, as we’ve said already, this is the number after another number has been rounded to the nearest hundred. So to begin with, we need to think about our hundreds digit. It’s been rounded to a two. But what could it have been?

Well, there’s only two possible answers to that question. It could’ve been a one, and our starting number could be ninety-five thousand one hundred and something, in which case our number would’ve been rounded up to 95,200. Or the hundreds digit could be a two, ninety-five thousand two hundred and something, in which case we’d be rounding down to 95,200. But let’s not forget we’re looking for the smallest whole number. The hundreds digit we’re looking for then is one. But how many tens should our number have?

Do you remember the rule about digits for rounding? If a digit is four or less, we round down. And if a digit is five or more, we round up. If our tens digit was a nine, for example, our number would be ninety-five thousand one hundred and ninety something. This would round to 95,200. But we can go smaller than the nine in the tens place because an eight would round up too, and a seven, a six, and we can go one lower because we know if a digit is five or more, we round up. So the lowest possible tens digit is five. Ninety-five thousand one hundred fifty something is definitely going to round up to 95,200. It doesn’t matter what the ones digit is. It’s still going to round to the number we want.

But wait a moment! It does matter what the ones digit is because we’re looking for the smallest whole number. There’s no point putting the digit nine in there. We could go lower than that. We need to put the smallest possible value digit, which is a zero, 95,150. Now, we know that 95,150 is actually exactly halfway between 95,100 and 95,200. But with rounding, when we’re looking at a number exactly at the halfway point, we always round up. We’ve looked at the value of each digit in a five-digit number and used this to help us think about rounding. The smallest whole number that if we rounded to the nearest hundred will give us a result of 95,200 is the number 95,150.

So what have we learned in this video? We’ve learned how to round whole numbers within one hundred thousand using number lines and thinking about each digit’s value.

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