In this lesson we're going to look at multiplying with decimals. So here we're going to multiply eight and 24 hundredths by three and six tenths. We're going to set it up so that the numbers are one on top of the other so we can do column multiplication. Now notice we are not concerned with lining up the decimal points when we multiply. The decimal points don't have to be lined up. When we add or subtract decimals, they do have to line up perfectly. But with multiplication it does not matter. So now we can go ahead and just focus on multiplying the numbers. So we start with the six. Four times six is 24. Bring down the four, carry the two. Two times six is twelve. Add that two, we get 14. Bring down the four, carry the one. And then eight times six is 48. Add that one, we get 49. Now we're going to go to the next row and multiply with the three. But first let's cross off the one and two that we carried up top because we don't need those anymore and we don't want those to confuse us with the next step. We go to the next row, place our zero under the last digit as our placeholder and we can multiply with the three. Three times four gives us twelve. Bring the two down, carry the one. Three times two is six, add that one, we get seven. And eight times three is 24. Now we can add, we get our total 39664. It doesn't have the decimal point. That's what we need to figure out - where that decimal point will go in our product. Now to figure that out we need to count how many digits are after the decimal points and the numbers that we multiplied. If we look at the numbers that we are multiplying, we have 8.24 that has two digits after the decimal point and then the 3.6 has one digit after the decimal point. So we have three digits altogether that are after the decimal point. That's going to tell us where the decimal point goes in the answer because our answer will also have to have three digits after the decimal point. So if we place it right there after the nine, we do have three digits after the decimal point. So our final answer is 39 and 664 thousandths. Now let's see what happens when we multiply a decimal by a power of ten. Powers of ten are numbers that have a one followed by one or more zeros. So that's one way that you can recognize them. Once you learn more about exponents, you'll learn that powers of ten are equal to ten raised to the first power, ten squared, ten cubed, et cetera. But the simple way to recognize them is that they have a one followed by one or more zeros. So we have ten, 100, 1,000, 10,000 and we can go on and on forever. Now let's see what happens when we multiply a decimal by a power of ten. So first we have 9.7654 times ten that's going to equal 97.654. So notice that the decimal point really just moved to the right one place value. Instead of being after the nine, now it's after the seven. If we multiply that same number by 100. Now the decimal point moves two places to the right so that it's after the six. And if we multiply by 1000, it'll move three places to the right. Now it's after the five. So do you see the pattern here? Well, the pattern is that the decimal point will move to the right when we move multiply by a power of ten. And to figure out how many place values it will move, we can really just count how many zeroes are in the power of ten. So for example, when we first multiplied by 10, 10 has just 1 zero in it. So that means the decimal point will move one place value to the right. When we multiply by 100, since 100 has two zeros in it, the decimal point moves two place values to the right. And when we multiply by 1000, since 1000 has three zeros, the decimal point moves three place values to the right. So now you know how to multiply decimals and how to multiply decimals by powers of ten.