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Long division with decimals

How do we divide a decimal by another decimal? One great approach is first to turn both numbers into whole numbers before proceeding with the standard algorithm. Sal Khan shows us how to do this. When using long division, it is important to keep things organized and in neat columns!

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Video transcript

- [Voiceover] Let's figure out what 2.211 divided by 6.7 is. So the first thing I like to do is, I don't like to divide by a decimal. So I'm going to multiply 6.7, I'm going to multiply 6.7 by 10, which is essentially just taking this decimal and moving it one space to the right. Well I can't just do that to the 6.7, I also have to do that to the 2.21. So let me move its decimal one space to the right. And so now I can rewrite the problem. I can rewrite it as 22, 22 point, 22.11 divided by, divided by, instead of writing it as 6.7 I can now write it as 67. 67, let me do it in that same color. I can now write it as 67. I could write a decimal right over here but that's not going to change the fact that this is just now the whole number 67. And so now I'm ready to do some long division now that I'm dividing by a whole number. You might say, "Wait, I still have a decimal over here," but that's okay and you're going to see that in a second. So let's try to do some long division. So we're going to take, we're going to take 22.11 or 22 and 11 hundredths, and we are going to divide, let me write that a little bit bigger just so we have some space. 22.11, and we are going to divide that by... We are going to divide that by 67. 67. Alright, let's do some long division now. And actually, before we even do that, I like to keep track of my decimal. So my decimal is over here, I'm going to write my decimal right over here in the answer. And when you're doing these long division problems it's really important to write things neatly and keep things in nice columns and keep track of your place value because if you don't write things in neat columns then frankly you'll probably lose track of your place value. But let's do this. So 67 goes into 2 zero times, so let's move on. 67 goes into 22 zero times. 67 goes into 221. So let's think about that a little bit. This is pretty close to 70, 70 times 3 would be 210. So this looks like maybe three times, three times seems about right. So let's try, let's put a 3 up here. 3 times 7 is 21, carry the 2, 3 times 6 is 18, plus 2 is 20, is 20. So we get 201 and the difference between 221 and 201 is going to be... Well you just get a 0 here, you get a 2 here, then you get a 0 here, I don't have to write it. It's 20. So 3 was right, if 3 times 67 were higher than 221 then we'd be in trouble. And then if 3 times 67 were lower but it was so low that when you subtracted you got a number higher than 67 then that means you could have thrown in more 67s in there, but this number's just right. It's lower but our remainder is less than, is less than 67, so let's keep going. So now we can bring down, we can bring down the 1 and we see 67 goes into 201, well we just figured that out. 67 goes into 201 three times, three times. 3 times 7 is one, carry the 2, gotta make sure we don't... Well, if we're doing the same problem as we did before but it's good to not have the previous 2 there, sometimes you might want to erase it. Then you have 3 times 6 is 18 plus 2 is 20. And now you subtract, and we are done because we have no remainder and there's nothing here left to bring down. And so 22.11 divided by 67 is... And we can throw a 0 here just for good measure. It's 0.33. 0.33, this is equal to 0.33. Or this is equal to 0.33. And we're done.