Rounding to the nearest 10

In this video, we're going to be doing some rounding, which you're probably not familiar with just yet. But you'll see that it's pretty straightforward, and we're going to start by rounding to the nearest 10.

So the first question is, what is rounding and why is it even useful? Well, let's say that you have the number 37. It's a fine number, but let's say that you have to do some math with the number 37. You can do a lot of math with the number 37, but let's say you just want to estimate what something might be. Let's say that someone says, "Hey, I have 37 pickles, and you have 39 pickles." Roughly how many do we have together? We don't have to have it down to the exact number of pickles. Well then, rounding will actually be a very useful tool.

But let's just focus on what it means to round to the nearest 10. So when they're talking about rounding to the nearest 10, we're going to be thinking about the tens place of the number. So we can see right over here in our tens place, we have a three. That three represents three tens. So the number 37 has three tens and seven ones. It is more than three tens and going to be less than four tens.

So this number is going to be more than three tens. I could do it like this: it's going to be more than three tens, which we can represent like that—three tens, zero ones—or you might know that as 30. It's going to be less than four tens, or also known as 40. And so when you're rounding, you're either going to round to the number of tens that is right below this number or the number of tens that is right above that.

But how do we know whether 37 rounded to the nearest 10 is going to be 30 or 40? Well, to answer that question, let's first just do it visually on a number line, and then we can come up with some rules for ourselves.

First of all, let's just count by tens and make sure we include 30 and 40. So if we start at 0: 0, 10, 20. Actually, let me have a little bit more space because I want to see the interesting things that are going to go on: 0, 10, 20, 30, 40. That's enough, but I could just go to 50 just to complete this number line.

So where is 37 on this number line? Well, it's between 30 and 40. If I wanted to make it a little bit clearer, if I said that this is 35 right over there, right in between 30 and 40, then 37 is going to be right about here. So that is 37.

When you're rounding to the nearest 10—and remember we're picking between three tens and four tens—you say which ten is it closest to? Is it closer to three tens or is it closer to four tens? Well, you can just look at this and say, "Hey, it looks a lot closer to four tens." So in this situation, 37 rounded to the nearest 10 is going to be 40.

You might ask a question: "Well, give me another number. What if someone said, '32 rounded to the nearest 10?'" Well, 32 is going to be right over here, and then you'd say, "All right, well that's between three tens and four tens, but it's a lot closer to three tens." So 32 rounded to the nearest 10 is going to be 30.

Now, an interesting question that you might be wondering is, what if you're right in between? What if we wanted to round 35 to the nearest 10? 35, once again, it's between three tens and four tens, between 30 and 40. Which one do we round to if we want to round to the nearest 10? Well, the rule is—and this is really just something that society has decided on—is that if you're right in the middle, you round up.

So the number 35 is going to round up to 40. Even though it's exactly 5 away from each of these numbers, 35, if you're right in between, is going to round up to 40. If you're a little bit less than 35, then you're going to round down to 30.

With that out of the way, let's do some more examples. Let's do, actually, an example of a three-digit number where we're rounding to the nearest 10. Let's say that we want to round the number 124 to the nearest 10.

Well, you could—there's a couple of ways that you could think about this. You could say that this is 100, two tens, and four ones. Or you could even view this as 12 tens and four ones. So you could say, "Hey, this is in between 12 tens and four ones." It's greater than 12 tens, which is 120, and it's less than 13 tens, which is 130. These are the two tens that are closest to this number.

Then, to decide which one it rounds to, you might already be able to think about it based on some of the rules we came up with, but let me draw it on a number line for you. So let me draw a number line, and I'm not going to start at 0 because we all have to get all the way to 130. So let's just start—I’ll start at 100. This is 100, 110.

Let me draw the number line: we're going to have 120, then we go to 130. I'll just do 140 here just for filling out the number line that I've drawn so far. Then I'll draw the halfway mark, which is 125.

See, it's halfway—maybe a little bit closer to there—and then 124. Let me do it in this red color: 124 is right over there.

So for trying to pick between 120 and 130, between 12 tens and 13 tens, which one is it closer to? Well, we can see it's only four away from 120, while it's six away from 130. So we would round down. We're going to round down to 120 in this situation if we're rounding to the nearest 10.

If this was 125 or 126, 127, 128, or 129, well then we would round to 130. And of course, if it was 130, we would round it to 130.

Let's do one more example, and actually I'm going to do a one-digit number. Let's say we want to round 7 to the nearest ten. So I'll write it out: round 7 to the nearest ten. Pause this video and see if you can do that.

All right. Well, 7 is between what two tens? Well, 7 is less than one ten, so it's less than one ten, and it's greater than zero tens. So it's between zero tens, which is just 0, and one ten, which is 10.

But which one does it round to? Well, here once again we can draw our number line. So we'll do 0, and then this is 5, and then this is 10, and 7 is right about there. That is where 7 is.

We can either visually see that 7 is closer to 10 than it is to 0. It's only 3 away from 10, while it's 7 away from zero. So you would round up to 10. Or you can use the rule that we just thought about: 7 is greater than or equal to 5, so you round up.

You round to the 10 that is higher than this number. If this number was—in the ones place—I can say if your ones place is between zero, it's greater than or equal to zero but less than five, then you round down.

You can see that happens in all of these situations. If you looked at 37, you look at the ones place, and your ones place here is greater than or equal to 5, so you round up. Here, if your ones place is equal to five, once again, you round up. If your ones place is less than five, well in this situation, we round down. If your ones place is less than five, you round down your ones place.

And here you only have a ones place, but it's greater than or equal to five, we rounded up.