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Estimating multi-digit multiplication

Learn the skill of estimating the product of multi-digit numbers. Watch a demonstration of the process. The video emphasizes the importance of estimation in simplifying complex multiplication problems.

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Video transcript

- [Instructor] What I would like to do in this video is get some practice estimating the product of multi-digit numbers and there's no better way of getting practice than just trying it ourselves. And so right over here, it says estimate 29 times 3,198. Why don't you pause this video and try to estimate this? And of course you can do this by multiplying this out on paper or using a calculator, but this is a useful skill, try to do it in your head. See if you can estimate what this is going to be. Well, before even looking at these answers, I would say this is going to be approximately equal to ... Let's see, 29 is awfully close to 30, and then I could multiply that times, I could either multiply that times 32 hundred, which is awfully close to 3,198, or if I wanted an even more rough approximation, I could say that's roughly equal to 30 times three thousand. So if I did 30 times three thousand, three times three is equal to nine, and then I have one, two, three, four zeroes. One, two, three, four zeroes. And actually my approximation, it turns out, is here, right over here, 90 thousand. Now if I wanted a slightly better approximation, I could have said this is approximately equal to 30 times 3,200, and this you could also do in your head. You could say, well, what is three times 32? Well, that is gonna be 96, and then you have one, two, three zeroes. One, two, three zeroes, so this would be a slightly better approximation, and if this is what you got, the closest answer here is still going to be equal to 90 thousand. Let's do another example. So here, we are asked to estimate 137 times 18. So pause this video again and see if you can come up with an estimate. Try to do it in your head. Well, there's once again many ways of trying to tackle it. The way I would tackle it, I would say, well, that's pretty close to 140 times 20, and then this would be equal to 14 times two is 28, and then we have two zeroes here, so that would be roughly 28 hundred, but when I look over here, there is no 28 hundred, and so maybe the closest one right over here is two thousand, so that would be my, that could be an approximation. Another way, it looks actually the way that they did it, they even did a coarser approximation, they rounded this to the nearest hundred, and so they said this is approximately equal to one hundred times and they rounded this to the nearest ten, one hundred times 20 which is even easier to do in your head, which is equal to two thousand, which is this choice that they got right over here.