Decimal place value with regrouping

We're told that "Each square below represents one whole." So this big square right over here is a whole, and then this big square over here is another whole. Then they ask us "Which of the following does the shaded area represent? Select all that apply." So let's see-- the shaded area. We're shaded in blue. So let's see-- one way to think about it is we have 1 whole over here. and then over here we've divided it into tenths: there's 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 equal sections, and we've shaded in one of them. So we've shaded 1 tenth. So this would be 1 whole and 1 tenth. So we could say that this is 1 and 1 tenth. So that's one way to think about it, but what about these other ones? Well even this one has been divided into tenths, and you can view 1 whole as 10 tenths. You see that here, where we've divided it into 10 equal sections. 10 tenths, and we've shaded all 10 tenths in. So this whole you could view as 10 tenths: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. And then we have an 11th tenth. So we have-- if you count these blue rectangles, we have 11 tenths. So you could also write this as 11 tenths. Now 11 hundredths? No, I don't think-- we haven't even divided this into hundredths, and 11 hundredths would be a little more than 1 tenth. And so this is definitely way more than that. So I could check my answer (and actually you don't see it but it's happening off-screen) but this is what I would go with for that. Let's do a couple more of these. So it says "Which of the following describes the location of the point on the number line?" Let's see. I have 1, and then between 1 and 2 I've divided it into 10 equal spaces. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. So each of these tick marks, or hash marks, is going to be a tenth. So this is 1 and 0 tenths, 1 and 1 tenth, 1 and 2 tenths, 1 and 3 tenths, 1 and 4 tenths, 1 and 5 tenths, 1 and 6 tenths, 1 and 7 tenths, 1 and 8 tenths. So 1 and 8 tenths is the same thing as 1.8. 1 and 8 tenths. So it's that. But what about these other options? Well one way we could think about this is-- let's just count the tenths. Each of these hash marks is a tenth. So 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. It makes sense. A whole is 10 tenths. Let's keep going, we were at 10 tenths. 11 tenths, 12 tenths, 13 tenths, 14 tenths, 15 tenths, 16 tenths, 17 tenths, 18 tenths. This one also applies. 18 hundredths: this would be between 10 hundredths and 20 hundredths which would be the same thing as between 1 tenth and 2 tenths. So 18 hundredths is going to be someplace around here, so I definitely will not select that one. Let's try a few more of these. So they say "Write a decimal that is equal to 24 tenths." Alright, 24 tenths. So remember we could view this as-- I'll just write it down-- we could view this as 20 tenths plus 4 tenths. But what is 20 tenths equal to? 10 tenths is equal to a whole, so 20 tenths is going to be equal to 2 wholes. So this could be viewed as 2 plus 4 tenths, or another way to write this-- we could just write 4 in the tenths place. So we could just write this as 2.4. 24 tenths: 20 tenths are 2 wholes and then you have another 4 tenths. Let's do one other one. "102 hundredths." So we could rewrite this as 100 hundredths plus 2 hundredths. Now, what is 100 hundredths? Well 100 hundredths is equal to 1, is equal to a whole. So 100 hundredths is just equal to 1. So you could view this as 1 plus 2 hundredths. Another way to write two hundredths is 0.02. So what's 1 plus 0.02? Well it's just going to be 1.02. And you see that here. You have 1 and 2 hundredths. 1 is the same thing as 100 hundredths. So this is 100 hundredths and you have 2 hundredths gives you 102 hundredths. Alright, let's do another one. "What is 32 tenths written as a decimal?" So we just have to remind ourselves: 10 tenths is equal to a whole. 20 tenths is equal to 2 ones. 30 tenths is equal to 3 ones. So this is going to be equal to 3 ones and then another 2 tenths. 3 ones and another 2 tenths. Let's keep going. "What is 203 hundredths written as a decimal?" Well we have to remind ourselves that 200 hundredths is equal to 2 ones. So here this is the same thing as 2 ones and 3 hundredths. 2 ones-- this case right here-- 2 ones and 3 hundredths. Let's do a couple more of these. "1.05 is equal to how many hundredths?" Well, one whole, or 1, is equal to 100 hundredths. So this is 100 hundredths plus 5 hundredths, or 105 hundredths. Alright. Let's do another one. "How can 2.60 be written in words?" So I could write this as 2 and 6 tenths. 2 ones and 6 tenths. I could also think of this as 2 ones and 60 hundredths. Or I could view this as 260 hundredths. So let's see which of these choices-- So "2 ones and 6 hundredths"... No, no, it's 2 ones and 60 hundredths, not 6 hundredths. It's 6 tenths right over here. 6 tenths or 60 hundredths. I won't select that. "260 hundredths." Yeah, that's right because 2 ones is that same thing as 200 hundredths and then we have another 60 hundredths right over there. So that's right. "260 tenths." No, 260 tenths-- remember 10 tenths is equal to a whole, so 260 tenths would be 26, would be 26 ones. So it's not that choice either. So anyway, I think we've done plenty of examples. Hopefully you have enjoyed that.