If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Lesson 5: Decimals in different forms

# Regrouping with decimals: 21.3

Practice the concept of representing decimals in different forms. Learn about place values, and how regrouping can change the appearance of a number, but not its value.  Created by Sal Khan.

## Want to join the conversation?

• What would be a practical application of this technique? Thanks.
• Say I have a stack of 1s (I get ones because the bus doesn't give change) and a 10. If I want to buy something that costs \$32, I need to figure out how many ones I need to come up with this amount with the 1 ten. Well, 20 is the same as 20 ones, so I could use the 1 ten and 22 ones to pay for my item.
• i dont get why you would regroup over 2 places instead of just one and i also dont get why you would nonly give 9 to the tens place and only 1 to the tenths place?
• Say you are subtracting two numbers such as 213 - 167. Borrowing from the tens place is no good at first since there isn't enough value in the tens place to cover its own subtraction let alone having excess to borrow from, so you would need to borrow 100 from the hundreds place instead and you can either give it all to the tens place first and then borrow 10 of that to give to the ones place or you can combine the steps and give each place what they need from the 100, in this case 10 to the ones place and the remaining 90 to the tens place.

It is the same idea in the video, except he brings a decimal place into it and doesn't do it in the context of subtraction in order to keep things simple for now.
• At he takes 1 directly from the tens place and puts it in the tenths place. He says its equal to 13/10 but wouldn't it be equal to 103/10 since its drawn from the tens to the tenths place?
• Well here, he is taking a 1 from the tens place and taking that one and adding it to 3 tenths. He's basically regrouping the number one. Take the one from 21 and it leaves you with 20, then add that one to the number to the right of it. So lets say that I have 26.4 or something like that and I want to regroup it. Well right now we have 20 + 6 + 4/10. We can take the 6 in 26.4 and take away 2 which leaves us with 4.
6-2=4.So now we have 24.4, but we still have that 2. You might ask what do we do with it, I'll show you. So the number to the right of six is 4. This is something that is really important: you are always regrouping the number to the right of the number you took away from. So using that 2 we add it to the 4. Our answer is 24.6, easy as pie.

So really what we learned is that another way to write 26.4 is 24.6. It's basically the same thing. Try it and you'll get it. I believe in you Doak. You need to have a positive mindset and be able to understand. Watch that part of the video if you have to. But do it, and you'll get it. Hopefully this was a help to you, Mr. Doak.
• Does anyone ever end up doing addition in hundreds by accident😅
• yes I did
• can we expand 999999999999999999.444444444444444444444444444444444444444444444444446666666666666666666666666666655555555555555555999999999444444444488888888888888888888888888
• Yes, but its gonna take a long time.
• converting decimals to fractions?

In this video, Sal does sometimes convert decimal place values to fractions. We do this all the time when we subtract, especially with decimals. Let's say you have 1.3 and you need to subtract 0.8.
` 1.3`
`-.8`

Well, 1.3 is the same as one plus 3 tenths, which is the same as 1 + 3/10. 0.8 is 8 tenths. I cannot directly subtract 8 tenths from 3 tenths because there aren't enough tenths.
` 3 tenths` minus `8 tenths`
hmmm..

In this video, Sal showed us how to make more tenths by regrouping from the other places in the number. We have a 1 that we can make into more tenths. How many pieces do you get if you divide one into ten equal pieces.
Easy! Ten pieces. So, we can get 10 more tenths to help out in the war against 8 tenths.

Now we have 13 tenths

`13 tenths` minus ` 8 tenths`
Well, that leaves 5 tenths which we can rewrite as 0.5

So
` 1.3`
`-.8`
__
`0.5`
• How did the 3 become a 13, if you were just adding 1?
(1 vote)
• Good question!
The 1 is in the Units place, but it is 10 times bigger than the 3 because the 3 is in the Tenths place. Therefore, the 1 will count as 10 when moved to the Tenths place making 13 when added to the three.

If the number in the Units place was a 2, this would count for 20 times the number in the Tenths place.

Hope this helps.
• dog the best animal upvote if you agree
• I can solve the problems about this, but I really don't get the point, and when I don't get it, I forget it later... Question? Why would I need two digit number in tenths place?? Doesn't that make tenths and hundredths?
• There is a two digit number in the tenths place because this is regrouping, which is just representing the number in a different way, with the number still being equival to its original form. Regrouping is used a lot in addition, subtraction, and multiplication, but you would not write a number as the regrouped version of itself in many cases other than addition, subtraction, and multiplication problems.

Sal meant that the number is 20 and 13 tenths, which is the same as 21 and 3 tenths, because when you have ten or more tenths, it represents one or greater.
13 tenths written as a fraction is 13/10, which, when simplified is 1.3.
This would not create tenths and hundreds, because 1 of the value of the number in the ones place was being moved into the tenths place, but the tenths were not moved over to the hundredths place, as that would create a different number, which would not be the same as regrouping the number. Remember, when you regroup a number, it always has to be equal to the original form.
• im bored
like 4 vidios in a row.

## Video transcript

I want to think about all of the different ways we can represent value in the number 21.3. So one is to just look straight up at the place values. This 2 is in the tens place, so it literally represents 2 tens. So this is equal to 20, 2 times 10. This 1 is literally equal to 1. It's 1 one. And then this 3 is 3/10, so plus 3/10. But now I want to rearrange or regroup the value in these places. So, for example, I could take 1 from the ones place and give it to the tenths place. So let's see how that would work. So we're going to take 1 away from the ones place, and so it's going to become a 0. And we're going to give it to the tenths place. And what we're going to see is that that's going to make the tenths place into 13/10. Now, does that actually make sense that I took 1 from here and it essentially added 10 to the tenths place? Well, let's rewrite what this represents. So we still have 2 tens. So this is still going to be 2 tens. Now we have plus 0 ones. And we essentially wanted to write that 1 that we took away from the ones place in terms of tenths. So if we were to write this in terms of tenths, it would be 10/10 plus the 3/10 that were already there. And so this is going to be equal to 13/10. Let me write that down. So this is equal to 20. That's the color you can't see. This is equal to 20 plus 0 ones, so 2 tens plus 0 ones plus 13 tens. Let's do another example with this exact same number. So once again, 21.3. And I'll write it out again. This is equal to 20 plus 1. We'll do that in the purple color. Plus 1 plus 3/10, plus 3 over 10. Now, I could take 1 from the tens place so that this becomes just 1. Now what do I do with that 10? Well, let's say with that 10 I give 9 of it to the ones place. So I give 9 of it to the ones place so that this becomes 10. And I still have 1 left over, and I give it to the tenths place, so that's going to become 13/10. So what did I just do? Well, I could rewrite this. Let me be clear what I did. This is the same thing as 1 plus 9. Actually, let me write it this way. 1 plus 9 plus 1. That's obviously the same thing-- 10 plus 9 plus 1 is the same thing as 20. And of course, we have what we have in our ones place, plus 1 plus 3/10. And what I want to do is I want to take this 9, the 9 that I took from the tens place and give to the ones place. And I'm going to take this 1 that I took from the tens place and give it to the tenths place. So 1 is the same thing as 10/10. And so when you regroup this value, you get this as being equal to 10 plus-- 9 plus 1 is 10, and then 10/10 plus 3/10 is 13/10. So that's all that happened here. I changed the value in the places. I took 1 ten away. I had 2 tens. Now I'm only left with 1 ten. And that extra 10 of value, I regrouped it. I gave 9 to the ones place. So 1 plus 9 is 10. And then I gave 1 to the tenths place. So 1 plus 3/10 is the same thing as 13/10.