Estimating decimal addition (thousandths) | Adding decimals | Grade 5 (TX TEKS) | Khan Academy

So we have two questions here, but don't stress out. Anytime I even see a lot of decimals, I'm like, okay, is this going to be a lot of hairy arithmetic? But what we see here, it does not say what 8.37 + 4926 is equal to. The equal sign is squiggly. That means, what is this roughly equal to? What is this approximately equal to? Or what can we estimate this sum?

So what I want you to do is estimate this sum, and then I want you to estimate this sum, and then we will work through it together. All right, now let's do it together. So the way I'll do this first one, I'm just going to round each of these to the nearest whole number.

So if I'm rounding to the nearest whole number, I could say, okay, is this going to be closer to eight if we round down, or is it going to be closer to nine? We know that it's a little bit more than eight, so it's between eight and nine. This is clearly, if we look at the ten's place, it's closer to eight than it is to nine.

So this is, I could say, approximately equal to 8. And then if I were to do that with the second number, we can clearly see, especially if we look at the 10's place, that this number is between four and five, but it is much closer to five than it is to four. So in this situation, we would round up. So this is going to be approximately equal to five.

So we could say this whole thing is approximately equal to, roughly equal to 8 + 5, which of course is 13. So if someone were to walk up to you on the street and said, "What's 8.37 plus 4926?" You’re like, "Oh, maybe I need some paper," say, "No, I just want a rough sense of what you think it is."

Well, okay, it's, you know, this is roughly eight, this is roughly five, this is going to be roughly 13. Well, let's do the same thing right over here. Well, here you might be tempted to say, okay, if we round to the nearest one, this one right over here is between zero and one. Well, this one we would maybe round up to one; this one is a little bit closer to zero than it is to one, so we round down to zero.

And maybe you say this is roughly 1 + 0, which is one, and that might be okay. But if you don't have any ones place here, it wouldn't make sense to round to the nearest one when you're approximating or when you're trying to get an estimate. Instead, I would round to the nearest tenth in this situation.

So for example, this first number right over here, 0.718, it's between 0.7 and 0.8. It's a little bit more than 0.7. And to realize which one it's closer to, you go to the hundredth place, you're like, okay, it's much closer to 0.7 than it is to 0.8. So I would say this is roughly equal to that.

And then I would do the same thing over here. I would look at the hundredth place. I know that this number here is between, let me do this in a different color, this number here is between 0.4 at the low end and 0.5. It's more than 0.4, and when you look at the tenth place, it's pretty clear that we're closer to 0.5.

So this first number is roughly equal to 0.7, the second number is roughly equal to 0.5. And so if I were to estimate the sum, what's 0.7 + 0.5? Or what's 710 + 510? Well, you might say, "Hey, that's 1210," and 1210 is the same thing as one whole and 2/10, or 1.2.

Or another way to think about it is 7 + 5 is 12, then 7 + 0.5 is 1.2, which you could do in your head if someone were to just walk up to you on the street and ask you that. And that's actually a pretty good approximation, a pretty good estimate.