Round 84516 to the nearest ten. Round 84516 to the nearest hundred. And round 84516 to the nearest thousand.
This problem tests our skills at rounding numbers. And it’s the same number that we’re being asked to round each time. Doing this is quite interesting because it helps us to see how the same number can change when we’re rounding to different amounts.
In the first part of the problem, we’re being asked to round to the nearest ten, then the nearest hundred, and finally the nearest thousand. We know that numbers live in certain places. They belong in a certain position. For example, this five-digit number here doesn’t belong between the numbers 20 and 25. It belongs with other five-digit numbers between 80000 and 90000. And that’s why visualising a number line with this problem can really help us to think about the position of this number.
We don’t have to draw a number line at all to solve the problem. We can just think about it in our heads. But for the purpose of this video, we will show the number lines just to show the sorts of things that we should be thinking about.
So the first part of the problem asks us to round 84516 to the nearest ten. So let’s visualise our number line. Which two multiples of 10 is 84516 in between? We can find the lower multiple of 10 quickly. We just need to change the six in the ones place for a zero, 84510. And if we add 10 to this, we get the multiple of 10 that’s greater than 84516, which is 84520. So we can say that where this number belongs is somewhere between 84510 and 84520. But which of these two multiples of 10 is it nearest to? Where would we round it to?
We know the midway point between these two numbers is 84515. But our number has a six in the ones place, 84516. So it’s greater than the halfway point. And we can see that it’s nearest to 84520. 84516 rounded to the nearest ten is 84520.
Let’s use the same method to consider the second part of the problem. This time, we’re being asked to round the same number to the nearest hundred. So again, we need to think about where 84516 lives, where it belongs. But this time, we need to think which two multiples of a hundred it lives between.
We know that multiples of hundred end in two zeros. So we can find the lower multiple of 100 by taking the one and the six from 84516 and just swapping them for two zeros, 84500. Then if we add 100 to this, we can find a number at the upper end of the number line. The two multiples of a hundred that the number 84516 is in between are 84500 and 84600.
Again, we can mark the halfway point to help us, which is 84550. We know that 84516 — we need to be looking at the digits one and six when we’re thinking about this number in particular — is a lot less than 84550. So we might mark it about here on the number line. We can now see that the nearest hundred is 84500. It’s only 16 away from this number. And so 84516 rounded to the nearest hundred is 84500.
Finally, we’re rounding to the nearest thousand. Multiples of 1000 have three zeros on the end. We can find the lower multiple of a thousand by taking the five, the one, and the six from our number and just swapping them for three zeros, 84000. We can then add 1000 to find the upper end of our number line. And so we can say the number 84516 is in between 84000 and 85000.
Always useful to find the halfway point, which is 84500. And we can see straight away that 84516 is slightly larger than 84500. So if we were to round this number to the nearest thousand, we’d get the answer 85000.
So in this problem, we’ve rounded the same number three different ways. And in doing so, we thought about where it belonged on the number line, which multiples of 10 it belonged in between, which multiples of 100, and which multiples of 1000. If 84516 is rounded to the nearest ten, it becomes 84520. If it’s rounded to the nearest hundred, it becomes 84500. And if it’s rounded to the nearest thousand, it becomes 85000.