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Regrouping with decimals

Explore the concept of expressing decimals in different forms. Delve into place value, regrouping, and how to represent the same decimal number in different ways using whole numbers. It's all about flexibility in understanding decimals!

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Video transcript

- [Instructor] We are told fill in the table with whole numbers to make 10.74 in two different ways. So pause this video and see if you can figure that out. So you really need to fill out what would you put in here for this to be a representation of 10.74? All right, now let's do it together and I'm gonna rewrite the number a little bit larger so we can really inspect the place values. So one way to think about it is we have zero ones and then we have one 10. But they don't express it that way. They don't say one 10 and zero ones up here. They just say 10 ones, but that's reasonable. So when they're saying 10 ones here, they are referring to those 10 ones, or you could view that as one 10 and zero ones. Either way, you have 10 ones, and then if you move one decimal place over, this 7/10, well that makes sense. You have a seven in the tenths place and then this 4/100 makes sense. You have four in the hundredths place. But now let's see what they're doing over here. So once again, they're saying no 10s, but 10 ones. So that is actually the same. We could say one 10 and zero ones, or we could say 10 ones. And now over here, they've reduced the number of tenths. You know, you're like, hey, what's going on? I have, there looks like there's 7/10 here. But one way to think about it is they're regrouping from one place to another. And so what they've done is they've taken that extra 10th and they've put it someplace. And the only other place they could put it is in the hundredths place. So if I were to take a tenth from the tenths place, a tenth is worth 10 hundredths. So one way to think about it is, you're taking a tenth from there, so now this is going to be, this is going to be 6/10, and if you, where you're going to put that tenth, well you could put it in the hundredths place, but a tenth is going to be 10/100. So if you add 10/100 to the 4/100 that are already there, well, that is going to give you 14/100, so we would put a 14 right over there. Let's do another example just to really make sure we're understanding what's going on. So once again, they say fill in the table with whole numbers to make 5.4 in three different ways. So pause this video and see if you can have a go at it. All right. So I'm gonna write the number, so we have 5.4, and in this first row, this is maybe the most standard way or traditional way of interpreting 5.4. In our ones place, you have a five and you see that, five ones, and in our tenths place, we have a four, and that's what they have right over here, 4/10. But what are they doing in this second row? Well, they're saying 24/10. 24/10, so somehow, in way to think about it, in the tenths place, they were able to add 20/10. So they went from 4/10 to 24/10. So if you're adding 20/10 here, they must have taken it away from some other place. 20/10 is the same thing as two ones, so they must have taken two ones away from here. So they took two ones away from here, so this would be three ones and now 24/10. So we could put a three right over there. And you can verify that. 24/10 is the same thing as two wholes and, or two ones and 4/10 or 2.4. 2.4 plus three is going to be equal to 5.4. All right. So here, we only have one one, and so what happened to the other four ones? Well, they must have been transferred to the tenths place. So let me rewrite the number. So if we were to take four ones away from the ones place, so we're taking four away from this, we only have one left, and what would happen if I transferred those four ones to the tenths place? Well, then there would be 40/10. Four ones are 40/10, so we would add 40 to 40/10 over here, so we already have 4/10, so this would become 44/10. 44/10. And we're done.