Visual understanding of regrouping decimals

- [Instructor] What we're going to do in this video is explore place value involving decimals, and in particular, we're gonna think about how you can regroup value from one place to another, which is gonna be very useful later in your life when you start doing some more arithmetic with decimals. So let's first think about what this number is right over here. So each square represents a one or represents a whole, so what number is this? Well, you could see that we have three whole ones, so we could write three, and then we have right over here, a whole is divided into 10 equal bars, these vertical bars, and so each of these are 1/10 and four of them are shaded in, so it's three ones, 4/10, and in this part right over here, we've divided a whole into 100 equal sections. It's a 10 by 10 grid, and we can see that one, two, three, four, five, six, seven of them are shaded in. So this represents 7/100, so this is 3.47, or three and 4/10 and 7/100 or three and 47/100. Now what we're going to do is explore how are other ways you can put the value into the different places? So let me set up a little table here. I don't think I'm gonna need all of that space, but we have, in this first example, so we have our ones, we have our ones place, we have our tenths place, and we have our hundredths, hundredths, hundredths place. I have to curve up a little bit. And so what we just did is we said, hey, this was pretty straightforward. This was three ones, three ones, 4/10, and 7/100, 7/100, but are there other ways that we could look at it? For example, is there a way of re-imagining this, so instead of three ones, we have two ones, and we still have 7/100, so how many tenths would we have in order for it to be the same value? Pause this video and think about that. All right, we'll do it together and to help us, I will put what we had here just now. Now what's different instead of having three ones, we now have two ones, so we could say that these are two ones right over here, our two ones. We have our 7/100 right over here. So essentially, we would have to express all of this in terms of tenths. So how would we express it all in terms of tenths? Well, this, what used to be a one, this is equivalent to 10/10. Let me make that very clear. I could, let me see if I could shade this in with that green color, so there you go. I'm gonna shade with the green color and then I'm gonna draw a bunch of lines here to make it very clear, so I'm just gonna hand draw it so one, two, three, four, five, six, seven, eight, nine, and 10. Did I do that right? One, two, three, four, five, six, seven, eight, nine, 10. And I didn't draw it as straight I need to. They really should be 10 equal sections, but it's hand drawn, so I think you understand. So notice. I took the exact same value, but I have regrouped. I have regrouped this one right over here into tenths. So how many tenths are here? Well, now I have 10 plus 4/10. So now I have shaded in 14/10. That was interesting. Let's do another example. So now let's imagine another scenario. Let's imagine a scenario where we have three ones again, but this time, instead of having 7/100, we have 27/100. So in that circumstance, how many tenths would we have? Pause this video and see if you can work it through. All right, well let's get that same number again. And now let's think about how we might have to regroup between the places. So we have our three ones, so that was just like the first case right over there, so we have our three ones. But now we have 27/100. So in addition to these 7/100, we have to find another 20/100 someplace. Well, the most natural place to go would be right over here and 20/100 is the same thing as 2/10. So what we want to do is we would convert these two tenths into hundredths, so let me actually just shade it in a little bit. So I'm going to convert this right over here to hundredths. And so did I do that right? One, two, three, four, five, six, seven, eight, nine, 10. And so there you have it. This plus this gives us our 27/100, and so how many tenths do we have left? We have 2/10, 2/10. So in this situation, we regrouped two from the tenths place and we expressed them as hundredths. So 2/10 became 20/100, added to the 7/100 that you already have and we now have 27/100. Hopefully that makes sense.