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Multiplying a Decimal by a Power of 10

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    A single postage stamp costs $0.44. How much would a roll of 1000 stamps cost?
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    And there is really a couple of ways to do it, and I'll do it both ways just to show you they both work.
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    One is a kind of a faster way, but I want to make sure you understand why it works.
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    And then we'll verify that it actually gives us the right answer
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    using maybe the more traditional way of multiplying decimals.
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    So, we're starting at $0.44. I'll just write a 0.44.
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    Well, that's one stamp, so this is one stamp. I'll write it like this, 1 stamp.
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    How much would 10 stamps cost?
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    Well, if 1 stamp is $0.44, then 10 stamps,
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    we could move the decimal to the right one place,
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    and so it would be, and now this leading zero is not that useful,
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    so it would now be $4.4. Or if you want to make it clear, it would be $4.40.
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    Now, what happens if you want to have a hundred stamps? 100 stamps.
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    Well, the same idea is going to happen.
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    We're now taking 10 times more so we're going to move to the decimal to the right once.
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    So, a hundred stamps are going to cost, are going to cost $44.00.
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    And this should make sense for you.
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    If one stamp is 44 hundreths of a dollar, then a hundred stamps are going to be
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    44 hundreths of a hundred dollars, or $44. Or you could view it as
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    we've just moved the decimal over one place.
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    So if we want a thousand stamps, if we want 1000 stamps,
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    we would move the decimal to the right one more time.
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    Moving the decimal to the right is equivalent to multiplying by ten. So then it would be $440.
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    Now, we could put, add another trailing zero just to make it clear that there is no cents over here.
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    So if you want to do it really quickly, you could've started with $0.44.
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    And you say, look, I'm not multiplying by ten. I'm not multiplying by a hundred.
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    I'm multiplying by a thousand. You're going to have to put another trailing zero over here.
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    And you would move the decimals from over here to over here.
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    You've essentially multiplied this times ten times ten times ten, which is a thousand.
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    So then this would become $440.
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    So let's verify that this works the exactly the same if we multiply the traditional way
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    the way we multiply decimals. So if you have 1000 times $0.44.
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    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.
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    Or you could just say, hey, this was 4 times a thousand.
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    Then we're going to go one place over so we're going to add a zero.
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    And we, 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.
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    Or we just did 4 times a thousand. So that is 4000,
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    if you don't include this zero that we added here ahead of time
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    because we're going one place to the left.
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    And then we have nothing left. I haven't at all thought about the decimals right now.
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    So far I've really just viewed it as a thousand times 44. I've been ignoring the decimal.
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    So if it was a thousand times 44,
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    we would get 0 plus 0 is 0, 0 plus 0 is 0, 0 plus 0 is 0, 4 plus 0 is 4,
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    4 plus nothing is 4. And if you ignore the decimal, that makes a lot of sense.
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    Because a thousand times 4 is 4000 and a thousand times 40 would be 40 000.
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    So you would get 44 000. But this of course is not a 44. This is a 44 hundreths.
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    We have, between the two numbers, two numbers behind the decimal point.
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    So we need to have two numbers behind or to the right of the decimal point in our answer.
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    So one, two. Right over there.
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    So, once again, we get $440.00 for the thousand stamps.
Title:
Multiplying a Decimal by a Power of 10
Description:

u3_l2_t2_we2 Multiplying a Decimal by a Power of 10

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Video Language:
English
Duration:
03:47

English subtitles

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