Question Video: Rounding Five-Digit Numbers Using a Number Line Mathematics

Look at the 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? If we round 14,189 to the nearest hundred, what do we get?

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Video Transcript

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.

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