In this lesson we're going to look at dividing decimals. Here's our first example. Eight and two tenths divided by five. So we have a decimal divided by a whole number. The first thing that we're going to do is set this problem up as long division. So we'll have 8.2 inside the division symbol as the dividend and the five in front as the divisor. The next thing that we want to do is line up the decimal point that's in the dividend with where we're going to have the decimal point in our answer, which we call the quotient. So we're going to just drag that decimal point straight up and that's going to tell us where the decimal point will be in our quotient. Now we can start doing our division. Five goes into eight one time. Five times one gives us five, subtract. We get three left over, then we can bring down the other two. We're not worried about the decimal point, just bring down the two. Five goes into 32 six times. Five times six is 30, subtract and we have a remainder of two. Now we don't want to have any remainders when we are working with decimals. So we're not really going to write this quotient as 1.6 with a remainder of two. Typically we're going to keep extending the digits out of that quotient, ideally until we don't have a remainder anymore. So this is how we'll do that. We're going to add zeros to the dividend. So right after that two that's in our dividend we're going to place a zero. Because remember that we can always add zeros at the end of a decimal and it doesn't change the value of that decimal number. So it’s perfectly fine for us to do that. And now that zero we can bring down. And now five goes into 20 four times. Five times four is 20. Subtract, now we have no remainder. So our final answer, our quotient is one and 64 hundredths. Our next example, we have two and 16 hundredths divided by 8 tenths. So this time our dividend is a decimal and our divisor is a decimal. We start off by setting it up with a long division just like before. Now when we have a divisor that's a decimal, we're going to change this a little bit first because we want that divisor to actually be a whole number just to keep the process simpler for ourselves. So all we're going to do is move that decimal point over one place to the right so that now our divisor will become a whole number. So now that decimal point moves over so that it's after the eight. Okay, now our divisor will be the whole number eight. Of course we can't just do that to the divisor. We also have to do it to the dividend as well. So we're going to move that decimal point so that it's after the one, just one place to the right. And what we're really doing mathematically is multiplying both of these numbers by ten. Multiplying by ten moves the decimal to the right one place. Okay, so now our problem becomes 21.6 divided by eight. And we have a whole number for our divisor, which is what we wanted. Now we set up everything just as before. We're going to align that decimal point up in the quotient, just drag it straight up from the dividend. And now we move forward with our division. Eight goes into 21 two times. Multiply, we get 16. Subtract, we get five left over. Bring down the six. Eight goes into 56 seven times. Multiply, we get 56. No remainder left. So our final answer is two and 7 tenths. Now, when we are dividing by powers of ten, remember, powers of ten are ten, 100, 1,000, 10,000, et cetera. We can just keep adding zeroes to the end to find more powers of ten. Let's take a look and see if we can find the pattern here. First number, we have 1234.5 divided by ten, which will equal 123.45. Now notice that the decimal point moves to the left one place value. If we divide that same number by 100, the decimal point moves two places to the left. So now it's after the two. And if we divide by a thousand, the decimal point moves three places to the left. So you see the pattern is very similar to what we saw when we were multiplying by powers of ten. Except when we multiply by powers of ten, the decimal point was moving to the right. This time when we're dividing, the decimal point is moving to the left. But to figure out how many place values the decimal point will move, you just count how many zeros are in the power of ten that you're dividing by. So when we divide it by 10, 10 has just 1 zero. So the decimal point moved one place to the left. Divide by 100 - since 100 has two zeros, we moved two places to the left and that pattern would continue on and on. So now you know how to divide by decimals and also how to divide decimals by powers of ten.