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## Regrouping decimal numbers

Current time:0:00Total duration:3:28

# Regrouping with decimals: 0.25

## Video transcript

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.