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### Unit 4: Lesson 11

Regrouping decimal numbers

# Regrouping with decimals: 0.25

Sal regroups 0.25 three different ways. Created by Sal Khan.

## Want to join the conversation?

• why did sal get one leaf not three
• The leaf stays after Sal answered the question, so he gets one leaf per one correct answer
• Is there another way to show the first example?
• I will give the first example in a similar way I already answered the question above. Writing 0.25 three different ways. We have a Tenths and a Hundredths fields. Remember each shift of a number to the left makes it ten times larger, so if we only put 0 in the first field of the second row and the total 0.25 was to be represented all in the Hundredths field it would have to write 25 time larger because 25x0.01 or hundredths=0.25. With the third way of writing it. If we only put 1 in the Tenths field, that is 10x0.01=0.1. That still leaves 25-10 hundredths or 15, so we wite 15 in the Hundredths field. The first row is easiest. If we put 2 in the Tenths field, that is 20x0.01=0.2. We still have left over 25-20=5, or 5 hundredths. We put 5 in the Hundredths field.
• how did he get one under the 2 I get the 2 and the 5 but he put a 1 under the two how did he get that and why did he put it there?
• At , does it matter what order you put it in? Could you put it as...
1 Ex. 2 1
1 101
0 201 -- as in the video

2 Ex. 1 101
0 201
2 1
Are they both Ok or do they need to be in order as in the video? --- Thanks to whoever answers this!
• I get it but I have a heavy book to do
• um I don't get how you "regroup" do you split up the number?
I am just not getting it...
• yes, you split it into an equation, ex: 100+10+1+1/10+1/100: 111.11
(1 vote)
• - was very helpful for me on a quiz.
#thankdevideos
• I don't think ill ever understand this :(
(1 vote)
• Hey Gannon, don't give up! :) Give it your best shot and ask the Khan community for guidance! Look up to the skies and seeee.....
Yeah, you can do this, yeah, oooh-yeah!
Yeah, you caaan dooo this, Gannon!
Look up, look up, look up, yeah, yeah!
Don't ya give up, no, no, don't ya give up!
We're all here for you, don't worry,
Yeah, so, DON'T GIVE UP! :D
(1 vote)
• when writing in the numbers in the problem why did sal why was it that all the numbers on the right were thought of as tenths
(1 vote)
• How do I regroup decimals in four different ways
(1 vote)

## 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.