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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.
• 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`
• Does anyone ever end up doing addition in hundreds by accident😅 • can we expand 999999999999999999.444444444444444444444444444444444444444444444444446666666666666666666666666666655555555555555555999999999444444444488888888888888888888888888 • 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.   