Regrouping with decimals: 0.25

Fill in the table with whole numbers to write 0.25 in different ways. So one way to look at it is just this 2 in 0.25 is in the tenths place, so it literally represents 2 tenths. While the 5 is in the hundredths place, so it literally represents 5 hundredths. So that's one way to represent it. But then we can start to rearrange value amongst these two place values. For example, what happens if we only have 1 tenth, then how many hundredths would we have to have? Well, 1 tenth is 10 hundredths. So if we take the 10 hundredths that we took away from here, and give it to the hundredths place, you're going to have 15 hundredths. And you could verify that 1 tenth plus 15 hundredths is equal to 25 hundredths. Or another way you could say it is 10 hundredths plus 15 hundredths is equal to 25 hundredths. Now another way you could do it, you could have no tenths and do it as all hundredths, because 2 tenths is the same thing as 20 hundredths. So 20 hundredths plus 5 hundredths is 25 hundredths. Let's do a few more of these. These are a lot of fun. Fill in the table with whole numbers to write 20.1 in different ways. So here, the table, the two columns are tens and tenths. So I guess the assumption is, is we're not going to give anything to the ones place here. And in the original example, we didn't have anything in the ones place either. So we could write the 2 in the tens place is literally 2 tens. And the 1 in the tenths place is literally 1 tenth. But let's think about what happens as we regroup value from the tens place to the tenths place. So if we only have 1 ten, then we have another 10 to play with that we have to express in terms of tenths. 1 ten is the same thing as 10 ones, which is the same thing as 100 tenths. So we're essentially giving 100 tenths. Notice, we have an extra 10 to play with, 10 of value. That is the same thing as 100 over 10, or 100 tenths. And we already had 1 tenth. So 100 tenths plus 1 tenth is going to be 101 tenths. I know it's really confusing. We have tens and tenths. So now let's go again. What happens if we take all the value in the tens place? So now we have 2 tens, or 20, to play with. Well, 20 is how many tenths? Well, you have 10 tenths per 1. So 20 is 200 tenths. And so you take the 200 tenths that you took out of the tens place. Add it to the 1 tenth. And you have 201 tenths. Let's do one more example. So let's write 2.1 in three different ways. So here it's between the one and the tenths place. So we could write it as 2 ones. And 1 tenth. We could also write it as 1 one. And now we've seen this game before. We have one extra 1 to play with. So that's going to be 10 tenths. Plus the 1 tenth that was already there, gives us 11 tenths. Or if we have no ones, well, 2.1 is the same thing as 21 tenths. The 2 represents, literally, 20 tenths. And then you have the 1 tenth. So 20 tenths plus 1 tenth is 21 tenths.