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# Dividing decimals completely

CCSS.Math:

## Video transcript

let's figure out what 6.3 divided by 0.25 is and when I look at something like this the first thing that I think about is well is there a way that I can rewrite this so instead of dividing it by 25 hundredths instead of dividing it by 0.25 I could divide it by a whole number maybe 25 and so how do I turn 25 hundredths into 25 well if I multiply it by if I multiply by 10 once then the decimal moves one spot to the right and if I multiply it by 10 twice then I'm going to move two spots to the right and 25 hundredths is going to become 25 I multiplied by 10 twice which is the same thing as multiplying by 100 now of course I can't only do it to 0.25 that would change the value of this entire expression I also have to do it to 6.3 if I move the decimal to the right twice over here to get a whole number I got to move the decimal twice to the right over here so let's see if I move it to the right once I get 63 so that's one multiplication by 10 and now I want to move it to the right again and you might say wait wait there doesn't look like there's any other digit here that I can move to the right of and we just have to remind ourselves it's six point three well that's going to be the same thing as six point three zero or we could actually add as many zeros as we want to the end of this and not change the value it's still six point three six and three tenths is the same thing as six and 30 hundredths so now I can move the decimal one more spot to the right and so I'm multiplying by ten again and it becomes 630 so six point three divided by 0.25 is the same thing as 630 divided by 25 let me do that again because this is really the tricky part or the artful part when you're dividing decimals if I were to write 0.25 being divided into being divided into six point three six let me do it six six point three now what I care about is moving this decimal to the right far enough so that this becomes a whole number I don't have to move it any further just far enough so this becomes a whole number and then I have to move this the same number of times to the right but the goal is to make this a whole number not to make the 6.3 a whole number although that is going to happen for this particular case so if I move it two spaces to the right so one to 0.25 becomes 25 and then 6.3 becomes would one space two spaces to the right it becomes 630 and so let me let me clarify that let me just clear all of this stuff our way out of the way to just make that clear what I just did so we don't have to deal with all this messiness when we're actually doing our long division now and so this one over here let me erase all of this business and we are ready to do some we're ready to do some some long division all right so now this is just straight forward dividing a two-digit number into a three-digit number and so we could say well 25 goes into 6 zero times so let's keep going 25 goes into 63 let's see 2 times 25 is 50 3 times 25 is 75 so that's too much so we want to go 2 times 2 times 25 is going to be 50 and we can subtract or if you didn't know 2 times 25 is going to be 50 you could have said 2 times 5 is 10 carry the 1 or regroup the 1 2 times 2 is 4 plus 1 is 5 so we got 50 and now we subtract and we get 3 minus 0 is 3 6 minus 5 is 1 and now we bring down the next digit we can bring down this is 0 and we could say 25 and let me scratch this out so I don't confuse myself later 25 goes into 130 how many times let's see 25 times 4 is 120 5 times 5 is 125 25 times 6 would be a hundred 50 so that's too big so I'm going to go 5 times so 5 times and I write it's very important to keep track of my places right here I brought down the 0 to make the 13 into 130 so when I say 25 goes into 135 times I write it above the oh I write it right above the zero right over there and then five times twenty-five five times five we already know what it is but I'll just figure it out five times five is 25 regroup the to five times two is ten plus two is twelve and now we can now we can subtract and you might know offhand well is 130 minus 20 125 is going to be five or if you like you could do a little regrouping you can make this you could take a ten from there and then put the 10 in the ones place and this becomes 10 10 minus 5 is 5 now we aren't done yet we want to divide this completely so we can bring down another zero we can bring down another zero and I'm picking an appropriate color too for the next so I'll use well I use the green once it will use yellow so once again I can bring down another zero but I have to be very careful you I can't just I can't just throw a zero right over there that's going to turn 630 into 6300 I have to be very particular say now to look look this next is zero I'm going to put that's going to be after the decimal now 630 is the same thing as 630 point zero and if I'm going to add a decimal there I want to throw the decimal right above it you need to be very careful with that but now we're ready to start bringing down the zero so let's bring down this 0 and we have a 50 how many times does 25 go into 50 let me scratch this out so you don't confuse ourselves later 25 goes 2 times into 52 times 25 is in fact 50 is in fact 50 and so now we can subtract and we now have a remainder of zero and there's nothing left to bring down other than zeros and we have a remainder of zero so we are done dividing completely you take 630 divided by 25 it's 25 point 2 or if you look at our original problem if you look at our original problem which was 6 point 3 divided by 0.25 that also is 25 point 2 2 so this is also going to be 25 point to let me rewrite it let me rewrite it so our original problem was 6 point 3 divided by 0.25 which we just figured out we just figured out is 25 and two-tenths and we're done