Estimating decimal multiplication

Let's now get some practice estimating multiplying with decimals. So first, here we have 7.8 times 307 is approximately equal to what? When you see the squiggly equal sign, that means approximately equal to one. What? So pause this video and see if you can figure out on your own.

All right, so the way that I would think about doing it, even if I was trying to, you know, do this in my head at the supermarket or something, I'd say, well, okay, this is—I probably need paper to do this properly—but gee, 7.8 is awfully close to 8, and 307 is pretty close to 300. So maybe I can estimate this by multiplying 8 times 300.

Now, this isn't going to be exact; it's definitely going to be off, but it's going to give me a good sense of roughly what 7.8 times 307 is. So what is 8 times 300? Well, 8 times 3 is 24, and so 8 times 300 would be 2400. We got these two more zeros, two more zeros, and so there you have it.

Luckily, the people who wrote this question estimated in a very similar way. Two people, when they estimate, might not get the exact same answer, but in this case, we happen to. Let's do another example.

So here we're trying to estimate 99.87 times 19. So pause the video again and see if you can come up with what a good estimation is. All right, so once again, not easy to do this in your head, but this 99 and 87 hundredths is pretty close—let me do this in a new color—this is pretty close to 100 times, and I could multiply 100 times 19. That's actually not so difficult.

So, for example, I could say 100 times 19 is equal to 1900. But notice we don't see that choice here. We could say, look, 1900 is definitely much closer to 2000 than any of these other numbers, so that might be a good approximation.

Now, how did they get 2000? Well, they rounded both of these numbers, they said this is approximately 100 times 20. So it's not that it's not that it's the right thing to do to round this 19 up to 20. If you could do 100 times 19, this is actually going to give you a slightly more accurate result than doing 100 times 20, but 100 times 20 is even easier to estimate in your head.

Either way, the closest choice here—and that's why I guess these have to be multiple-choice questions—is 2000. Let's do another example.

So here we are asked to multiply 2.21 times 5.1, and we want to know what it approximately equals. So once again, we are estimating, so pause this video and try to figure it out.

Well, we're just going to do the same thing we did in the last two examples. 2.21, and, well, first of all, this is hard to do in my head, and so 2.21, well, that's approximately—if I round to the nearest two or to the nearest 1, I should say—this is going to be 2 times 5, which is equal to 10. So this would be approximately equal to 10, and that is a choice.

Now, some of you might say, well, there are ways to get better estimations that you could still do with your head. So, for example, you could say that this is pretty close to—this is approximate—let me do it over here. This is approximately equal to 2 times 5.1. This is still pretty straightforward to do in your head; this would be 10.2.

But you'd still say that this is by far the closest one. Or you could even say something like this is approximately equal to 2.2 times 5. What is this going to be equal to? Well, 2 times 5 is 10, and 2 times 10 times 5 is another whole, and so this is going to be equal to 11.

So all of these might be things that you could estimate that you might be able to do in your head, but the important thing to realize is, however you do it, by far 10 is going to be the closest response to what you're getting at, and 10 would be a very natural estimation if you try to simplify both of these numbers when making that estimate.