Multiplying a decimal by a power of 10

A single postage stamp costs $0.44. How much would a roll of 1,000 stamps cost? And there's really a couple of ways to do it. And I'll do it both ways just to show you they both work. One is kind of a faster way, but I want to make sure you understand why it works. And then we'll verify that it actually gives us the right answer using maybe the more traditional way of multiplying decimals. So we're starting at $0.44. I'll just write it as 0.44. Well, that's one stamp. So this is 1 stamp. I'll write it like this, 1 stamp. How much would 10 stamps cost? Well, if 1 stamp is $0.44, then 10 stamps, we could move the decimal to the right one place. And so it would be-- and now this leading 0 is not that useful. So it would now be $4.4. Or if you want to make it clear, it would be $4.40. Now, what happens if you want to have 100 stamps? Well, the same idea is going to happen. We're now taking 10 times more, so we're going to move the decimal to the right once. So 100 stamps are going to cost $44. And this should make sense for you. If 1 stamp is 44/100 of $1, then 100 stamps are going to be 44/100 of $100, or $44. Or you could view it as we've just moved the decimal over one place. So if we want 1,000 stamps, we'd move the decimal to the right one more time. Moving the decimal to the right is equivalent to multiplying by 10. So then it would be $440. And we could add another trailing zero just to make clear that there's no cents over here. So if you wanted to do it really quickly, you could have started with $0.44. And you say look, I'm not multiplying by 10. I'm not multiplying by 100. I'm multiplying by 1,000. So you're going to have to put another trailing zero over here. And you would move the decimal from over here to over here. You've essentially multiplied this times 10 times 10 times 10, which is 1,000. So then this would become $440. And let's verify that this works exactly the same if we multiply it the traditional way, the way we multiply decimals. So if you have 1,000 times $0.44. So you start over here. 4 times 0 is 0. 4 times 0 is 0. 4 times 0 is 0. 4 times 1 is 4. Or, you could just say, hey, this was 4 times 1,000. Then we're going to go one place over. So we're going to add a 0. And once again, we're going to have 4 times 0 is 0. 4 times 0 is 0. 4 times 0 is 0. 4 times 1 is 4. Or we just did 4 times 1,000. So that is 4,000 if you don't include this 0 that we added here ahead of time because we're going one place to the left. And then we have nothing left. I haven't at all thought about the decimals right now. So far I really just viewed it as 1,000 times 44. I've been ignoring the decimal. So if it was 1,000 times 44, we would get 0 plus 0 is 0. 0 plus 0 is 0. 0 plus 0 is 0. 4 plus 0 is 4. 4 plus nothing is 4. And if you ignore the decimal, that makes a lot of sense because 1,000 times 4 is 4,000. And 1,000 times 40 would be 40,000. So you would get 44,000. But this, of course, is not a 44. This is a 44/100. We have, between the two numbers, two numbers behind the decimal point. So we need to have two numbers behind or to the right of the decimal point in our answer, so one, two right over there. So once again, we get $440 for the 1,000 stamps.