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Understanding decimal multiplication

This video introduces multiplying decimals, emphasizing the role of decimal placement in the product. It highlights the usefulness of estimation in simplifying calculations and understanding the relationship between the numbers. Created by Sal Khan.

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Video transcript

- [Instructor] We are told that 52 times 762 is equal to 39,624, and then we're told to match each expression to its product. And these products, this is an exercise on Khan Academy, you can move them around so the product can be matched to the appropriate expression. So pause this video and see if you can figure that out. All right, now what you might have realized is all of these expressions deal with the same digits as 52 times 762. They just have the decimal in different places. And so what we can do is, we can say, hey look, the answer is going to have the digits three, nine, six, two, four, in that order. And you could see all of these have the digits three, nine, six, two, four, in that order. And then we can estimate what these expressions should be equal to, what the products should be equal to, to think about the decimal. So this first expression, 0.52 times 76.2, the way I think about it is 0.52, that's close to 50/100, that's close to a half, and so 76.2, that's close to 76. And so this first expression, this first product should be roughly half of 76. Half of 76 would be around 38. And so which of these is close to 38? Well this first one is 39.624, so that's actually the closest to 38. The second one is 396. And then we have 3,962. So I like this first one, the 39.624. That feels right. Now the second expression, 0.52 times 762. Well once again, 0.52 is roughly equal to 50/100, roughly equal to 5/10, roughly equal to 1/2, and so, and 762, we could say hey, you know, that's, if we wanna be really rough, really, really approximate it, we could say, hey, it's roughly 800. And so this should be about half of 800, so it should be around 400. And so we actually had that choice already there. So this would be 396.24. Definitely wouldn't be the the 3,962.4. And so I'm already feeling good that this last choice sits down here. But I can verify it. 5.2, well let's just say that's roughly 5. 762, let's say that's roughly 800. So five times 800, that would be around, that would be 4000. And so we would expect this expression to be close to 4000, and indeed, that's what this choice is. So it turns out that it was already in the order that we needed it to be, but it's good that we checked on that.