Estimating adding large numbers by rounding

Let's say that we run an egg farm. Yesterday, we went out and we collected 398 eggs from the chickens, and then today we went out and we collected 251 eggs from the chickens. What we're curious about is roughly how many eggs do we now have that we've collected over the last two days.

Well, there's a few ways we could do that. We could just add 398 to 251 and figure out what that is equal to. But let's say that we don't have a lot of time, and we don't have paper, and we want to do it in our heads. We don't care about the exact number; we want to know roughly how many eggs do we have.

Well, that's where the tool of estimating is useful. Instead of saying the exact amount of eggs, we could say how many do we roughly have, and that's what this squiggly equal sign means. It means, hey, we don't have to get the exact number, but how many do we roughly have? So we will be estimating.

The way that we can do that is we can round each of these numbers to a number that is close to them but that's easier to add in our heads, and then we add those two numbers. So pause this video and see if you can do that on your own before we do it together.

All right, now let's do this together. Let's start with 398 and let's round it to the nearest 10. 398, you can view this as we have a 9 in the tens place, but you could view this as 39 tens and eight. The 10 that it is right directly above is exactly 39 tens and zero ones, or 390. The next 10 would be, if we go up to 40 tens, which would be the same thing as 400.

Now, which one would we round to? Well, 398 is closer to 400 than it is to 390. We've talked about in the rounding videos that you can see that this right over here is 5 or greater, so we would round the tens place up. So we would round to 400. Thus, 398 we round to 400.

Next, we're going to add that to 251. What's that rounded to the nearest 10? So I'll do that again right over here: 251. The 10 that is right below that is going to be 250, and the 10 that is right above that is going to be 260. Again, you could view this as 25 tens and 1.

251 is clearly closer to 250. We can round down. Another way to think about it is, you look at the tens place and then you look at the ones place and you say, hey, this is less than five, so I'm going to round down on the tens place. We get to 250.

So when you round 251 to the nearest 10, you're going to get 250. Now I encourage you to add these two in your head. What would this be equal to? Well, the way that I think about it in my head, there are a lot of different ways to approach addition.

But you could say, all right, I have, I can think about the hundreds. I have four hundreds and I'm adding that to 200. Let me do this in a new color. So if I have four hundreds and I'm adding it to two hundreds, well, that's going to be six hundreds.

If I have zero tens and if I'm adding it to five tens, well, I'm still going to have five tens. And then, I have zero ones in either case, so I'm still going to have zero ones. And so there you have it. We were able to estimate 398 plus 251 as being roughly 650.