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# Estimating decimal multiplication

CCSS Math: 5.NBT.B.7

## Video transcript

- [Instructor] 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 what. So pause this video, and see if you can figure it out on your own. Alright, so the way that I would think about doing it, even if I was trying to do this in my head at the supermarket or something, I'd say, well, okay, I'd probably need paper to do this properly, but gee, 7.8 is awfully close to eight, and 307 is pretty close to 300, so maybe I can estimate this by multiplying eight times 300. Now, this isn't going to be exact, it's definitely going to be off, but it's gonna give me a good sense of roughly what 7.8 times 307 is. So what is eight times 300? Well, eight times three is 24, and so eight times 300 would be 2,400, we got these two more zeros, two more zeros. And so there you have it, and 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 a good estimation. Alright, so once again, not easy to do this in your head, but this, 99 and 87/100 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 1,900, but notice, we don't see that choice here, we could say, look, 1,900 is definitely much closer to 2,000 than any of these other, so that might be a good approximation. Now, how did they get 2,000? Well, they rounded both of these numbers, they said, this is approximately 100 times 20. So, 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 gonna give you a slightly more accurate result than doing 100 times 20, but 100 times 20 is even easier to estimate in your head. But either way, the closest choice here, and that's why, I guess, these had to be multiple choice questions, is 2,000. Let's do another example. So here, we are asked to multiply 2.21 times 5.1, and we wanna 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 gonna 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 one, I should say, this is gonna be two times five, which is equal to 10, so this would be approximately equal to 10, and that is a choice. Now, some of you might say, "Whoa, there's 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 two times 5.1, this is still pretty straightforward to do in your head, this would be 10.2. And so, 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 five. What is this going to be equal to? Well, two times five is 10, and 2/10 times five 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.