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# Multiplying a decimal by a power of 10

## Video transcript

a single postage stamp costs 44 cents 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 a 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 44 cents I'll just write a 0.44 well that's one stamp so this is one stamp I'll write it like this one stamp how much would ten stamps cost well if one stamp is forty four cents then ten stamps we could move the decimal to the right one place and so it would be and now this leading zero is not that useful so it would now be four point four dollars or if you want to make it clear would be four dollars and 40 cents now what happens if you want to have a hundred stamps a hundred stamps well the same idea is going to happen we're now taking ten times more so we're going to move to the decimal to the right ones so 100 stamps are going to cost are going to cost forty four dollars and this should make sense for you if one stamp is forty four forty four hundredths of a dollar then 100 stamps are going to be forty four hundredths of a hundred dollars or forty four dollars or you could view it as we've just moved the decimal over one place so if we want a thousand stamps if we want a thousand stamps we'd move the decimal to the right one more time moving the decimal to the right is equivalent to multiplying by ten so then it would be four hundred and forty dollars now we could put add another trailing zero just to make clear that there's no sense over here so if you wanted to do it really click quickly you could have started with forty four cents and you say look I'm not multiplying by ten I'm not multiplying by a hundred I'm multiplying by a thousands 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 you've essentially multiplied this times ten times ten times ten which is a thousand so then this would become four hundred and forty dollars four hundred and forty dollars so let's verify that this works exactly the same if we multiplied the traditional way the way we multiply decimals so if you have 1000 1000 times 44 cents times 44 cents 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 a thousand then we're going to go one place over so we're going to add a 0 and we ate once again we're gonna 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 a thousand so that is 4000 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 distributed it as a thousand times 44 I've been ignoring the decimal so for 1000 times 44 we would get zero plus zero zero zero plus zero zero zero plus zero zero four plus 0 is 4 4 4 plus nothing is four and if you ignore the decimal that makes a lot of sense because a thousand times four is four thousand and a thousand times 40 would be 40,000 so you would get 44,000 but this of course is not a 44 this is a forty four hundredths 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 four hundred and forty dollars for the thousand stamps