Dividing decimals: standard algorithm
- [Voiceover] 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? 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 it by 10 once, then. the decimal's one spot to the right. And if I multiply it by 10 twice, then I'm gonna 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 a hundred. 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 gotta 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 wanna move it to the right again, and you might say, "Wait, wait, there doesn't look like "there's any other digits here "that I can move to the right of." And we just have to remind ourselves, that 6.3, well that's going to be the same thing as 6.30, or we could actually as many zeroes as we want to the end of this, and not change the value, it's still 6.3. 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 10 again. And it becomes 630. So 6.3 divided by 0.25 is the same thing as 630 divided by 25. And 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, 6.3. Six, let me do it. Six, 6.3. 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 that 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, two. 0.25 becomes 25, and then 6.3 becomes, move it 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 away out of the way, to just make that clear what I just did. So we don't have to deal with all of 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, alright. So now this is just straightforward, dividing a two digit number into a three digit number. And so we could say, well, 25 goes into six zero times, so let's keep going. 25 goes into 63, let's see, two times 25 is 50, three times 25 is 75, so that's too much, so we wanna go two times. Two times 25 is going to be 50, and we can subtract. Or, if you didn't know two times 25 is going to 50, you could have said two times five is 10, carry the one or regroup the one. Two times two is four, plus one is five. So we got 50. And now we subtract, and we get three minus zero is three, six minus five is one. And now we bring down the next digit. We can bring down this zero. 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 four is 100, 25 times five is 125, 25 times six would be 150, so that's too big. So I'm gonna go five times. So five times, And I write, it's very important to keep track of my places right here, I brought down the zero to make the 13 into 130, so I say 25 goes into 130 five times, I write it above the zero, I write it right above the zero right over there. And then five times 25, five times five, we already know what it is, but I'll just figure it out. Five times five is 25, regroup the two, five times two is 10, plus two is 12. And now we can, now we can subtract. And you might know offhand, well (mumbles), 130 minus 125 is going to be five, or if you like, you could do a little regrouping, can make this, you could take a 10 from there, and then put the 10 in the ones place, and this becomes 10, 10 minus five is five. Now, we aren't done yet. We wanna divide this completely, so we can bring down another zero. We can bring down another zero, and I'm picking an appropriate color, to, for the next, so I'll use, well I already used the green once, we'll use yellow. So once again, I can bring down another zero, but I have to be very careful here, I can't just, I can't just throw a zero right over there. That's gonna turn 630 into 6300. I have to be very particular, say no, look, look. This next zero I'm gonna put, that's gonna be after the decimal. Now 630 is the same thing as 630.0, and if I'm gonna add a decimal there, I wanna throw the decimal right above it. Need to be very careful with that. But now we're ready to start bringing down the zero. So let's bring down this zero. And we have 50, how many times does 25 go into 50? Let me scratch this out, so we don't confuse ourselves later. 25 goes two times into 50, two 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 25.2. Or if you look at our original problem, if you look at our original problem, which was 6.30 divided by 0.25, that also is 25.2. So this is also going to be 25.2. Let me rewrite it, let me rewrite it. So our original problem was 6.3 divided by 0.25, which we just figured out, what we just figured out is 25.2. And we're done.