Estimating multi-digit sums

- [Instructor] Let's get a little bit of practice estimating adding large numbers. So if someone were to walk up to you on the street and say quickly, roughly what is 493,792 plus 205,218, what does that roughly equal to? And sometimes people will put this little squiggly equal sign, that means approximately equal to what? And so you have to figure this out in your head. You can't get a piece of paper out and try to add place by place. So there's a bunch of ways that you could do this, but the way that I would do that is that both of these are in the hundreds of thousands. So in my head, I would round them to the closest 100,000 and then add them up in my head. So what I'm about to show you, I'm gonna write it down, but this is what I would be doing in my head. So 493,792, if I were to round that to the nearest 100,000, that's approximately equal to 500,000 and 205,218, if I were to round that to the nearest 100,000, that's approximately equal to 200,000. And now it's pretty easy to do in my head, 500,000 plus 200,000, well, that's 700,000. So this whole thing is approximately equal to 700,000. Now, let's give another example where the two numbers, one's in the thousands and one's in the tens of thousands. So let's say we have 64,895 plus 3,117. And once again, I just wanna estimate what this sum is equal to. I don't need to get the exact answer. How would you approach this? So it might be tempting to round this number to the nearest 10,000, which would get you 60,000 and then round to this number, to the nearest thousand, which would get you 3,000 and then add them together, you'd get 63,000. But something feels a little bit off there because you wouldn't expect 64,895 plus 3,117 to be less than 64,895. And the reason why we're getting that strange estimation is because if we're rounding one to the nearest thousand, we should round the other to the nearest thousand. So let's not do it this way, let's round them both to the nearest thousand. So 64,895 to the nearest thousand would be 65,000. And then in my head, I would say, okay, 65,000 plus 3,000 is going to be 68,000. So this is going to be approximately equal to 68,000.