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### Course: Arithmetic (all content) > Unit 6

Lesson 13: Dividing decimals: standard algorithm# 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!

## Want to join the conversation?

- Is Khan Academy good for studying? I feel it is and I am considering recomending it to a friend.(32 votes)
- Yes, Khan Academy is awesome!(22 votes)

- any easier ways to do this(11 votes)
- I would say probbally not:((7 votes)

- Is there an easier way to divide, without having to round and figure out what the closest number is and all that? Like how you do dividing only one digidt(9 votes)
- Unfortunately, there wouldn't be ):(0 votes)

- And when you have a decimal do you just erase the other decimal when you figured out your answer or just keep It there?(11 votes)
- hi, why do we add the numbers on top of the 67?(6 votes)
- For some reason this division is in 6 grade, but you actually learn this in 5th grade(6 votes)
- Bro you are not Sal Khan stop being an imposter !(1 vote)

- If there is a zero before a decimal can you just pretend it’s invisible(6 votes)
- What happens when you have a remainder in a problem like the one above? What do you do with the remainder?(5 votes)
- A few things:

You can just add it at the end (23r4, for example), but most of the time you're meant to turn it into a decimal, which will be shown in a later video. Sometimes, you also have to turn the remainder into a fraction or percent, but that is much less common.(2 votes)

- So you do not have to move the decimal place back to where your started, the correct answer is the same even with moving the decimal place at the start?(5 votes)
- multiply by 10(2 votes)

- Can you explain why moving the decimal point has no bearing on the answer. I understand it but can't articulatie to well to the class.

Love your work

Kind regards(2 votes)- I will gladly explain :)

Let's rewrite the equation in multiples or divisables of powers of ten. In our case 2.211 ÷ 6.7 could be rewriten as (2211 ÷ 10³) ÷ (67 ÷ 10) or (2211 ÷ (10 * 10 * 10)) ÷ (67 ÷ 10). We can cancel one of the tens on both sides like we would in a fraction. Remember from previous Khan Academy courses, where you find out ab/ac is the same thing as b/c? For the same reason we can do the same with division and remove the one of tens on both of the sides.

So to simplify: (2211 ÷ (10 * 10 * 10)) ÷ (67 ÷ 10) we can rewrite to (2211 ÷ (10 * 10)) ÷ 67. We also know 2211 ÷ (10 * 10) is 2211 ÷ 100 or 22.11.

So that's why 2.211 ÷ 6.7 can be simplified to 22.11 ÷ 67.

Hope that helps :D(8 votes)

## 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.