Multiplying a Decimal by a Power of 10

u3_l2_t2_we2 Multiplying a Decimal by a Power of 10

A single postage stamp costs $0.44. How much would a roll of 1000 stamps cost?

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.

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 $0.44. I'll just write a 0.44.

Well, that's one stamp, so this is one 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 zero 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 a hundred stamps? 100 stamps.

Well, the same idea is going to happen.

We're now taking 10 times more so we're going to move to the decimal to the right once.

So, a hundred stamps are going to cost, are going to cost $44.00.

And this should make sense for you.

If one stamp is 44 hundreths of a dollar, then a hundred stamps are going to be

44 hundreths of a hundred dollars, or $44. 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 1000 stamps,

we would 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 $440.

Now, we could put, add another trailing zero just to make it clear that there is no cents over here.

So if you want to do it really quickly, you could've started with $0.44.

And you say, look, I'm not multiplying by ten. I'm not multiplying by a hundred.

I'm multiplying by a thousand. You're going to have to put another trailing zero over here.

And you would move the decimals from over here to over here.

You've essentially multiplied this times ten times ten times ten, which is a thousand.

So then this would become $440.

So let's verify that this works the exactly the same if we multiply the traditional way

the way we multiply decimals. So if you have 1000 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 a thousand.

Then we're going to go one place over so we're going to add a zero.

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.

Or we just did 4 times a thousand. So that is 4000,

if you don't include this zero 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've really just viewed it as a thousand times 44. I've been ignoring the decimal.

So if it was a thousand 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 a thousand times 4 is 4000 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 44 hundreths.

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 $440.00 for the thousand stamps.