Regrouping with decimals

We are told to fill in the table with whole numbers to make ten point seven four in two different ways. So, pause this video and see if you can figure that out.

So, we really need to fill out what would be what would you put in here for this to be a representation of ten point seven four. All right, now let's do it together, and I'm going to rewrite the number a little bit larger so that we can really inspect the place values.

One way to think about it is we have zero ones, and then we have one ten. But they don't express it that way—they don't say one ten and zero ones up here, they just say ten ones. But that's reasonable! So when they're saying ten ones here, they are referring to those ten ones; or you could view that as one ten and zero ones. Either way, you have ten ones. Then if you move one decimal place over, this seven tenths—well, that makes sense. You have a seven in the tenths place, and then this four hundredths 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 tens but ten ones. So that is actually the same. We could say one ten and zero ones, or we could say ten ones. Now over here, they've reduced the number of tenths, and you're like, "Hey, what's going on?"

It looks like there are seven tenths here, but one way to think about it is they're regrouping from one place to another. What they've done is they've taken that extra tenth and they've put it someplace; 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 ten hundredths.

One way to think about it is they're taking a tenth from there. So now this is going to be six tenths. And where are you going to put that tenth? Well, you could put it in the hundredths place, but a tenth is going to be ten hundredths. So if you had ten hundredths to the four hundredths that are already there, well, that is going to give you fourteen hundredths. 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 five point four in three different ways. So pause this video and see if you can have a go at it.

All right, so I'm gonna rewrite the number. So we have five point four. In this first row, this is maybe the most standard way or traditional way of interpreting five point four. In our ones place, you have a five, and you see that five ones. In our tenths place, we have a four, and that's what they have right over here.

For tens, what are they doing in this second row? Well, they're saying 24 tenths. Twenty-four tenths! So somehow, in one way to think about it, in the tenths place, they were able to add 20 tenths. So they went from four tenths to 24 tenths. If you're adding 20 tenths here, they must have taken it away from some other place. Twenty tenths 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 tenths. We could put a three right over there. You can verify that 24 tenths is the same thing as two holes and or two ones and four tenths, or two point four. Two point four plus three is going to be equal to five point four.

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. If we were to take four ones away from the ones place, so we're taking four away from this; you only have one left. What would happen if I transfer those four ones to the tenths place?

Well, then they would be 40 tenths. Four ones are forty tenths. So we would add 40 to 40 tenths over here. So we already have four tenths, so this would become 44 tenths. 44 tenths, and we're done.