Let's try another example. Here we want to divide and round to the nearest thousandth. We have 519.37 divided by 86. 
So our dividend is 519.37. 
We're dividing by the divisor, which is 86. Now our divisor is already a whole number, so we don't need to move the decimal point there at all, which means we don't need to move the decimal point in our dividend either. We'll just put the decimal point in our quotient directly above where it is in our dividend. And now let's divide as we would with whole numbers. So 86 will go into 519 six times. 
And 6 times 86 is 516. We're going to subtract 516 from 519; that gives us 3. Bring down the 3. Well, 86 is bigger than 33, so it goes in 0 times. Zero times 86 is 0. Subtracting, we get 33. Let's bring down the 7. Eighty-six goes into 337 three times.
And 3 times 86 is 258. Subtracting that from 337 gives us a difference of 79. So we want to round to the nearest thousandth. Right now, we have a 3 in the hundredths place. So the next digit will be in the thousandths place, but we'll need to go one more after that to the ten thousandths place to know which way to round the digit in the thousandths place. So let's add a 0 to our dividend and bring that down. Eighty-six goes into 790 nine times.
And 9 times 86 is 774. Seven hundred ninety minus 774 is 16. So we need to go one more place to get our digit in the ten thousandths place. The 9 is in the thousandths place. We need to know whether we're going to keep that as a 9 or going to be rounding up. We'll bring that 0 down, and 86 goes into 160 just 1 time. The 86 times 2 would be 172. That would be too big. One times 86 is 86. Our difference here is 74, but we can stop. We see that, again, the number in the ten thousandths place is 1. So that means that the number in the thousandths place, the 9, is going to stay as a 9 when we round to the nearest thousandth. And so we can say that 519.37 divided by 86 is approximately 6.039 to the nearest thousandth.