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## 6th grade foundations (Eureka Math/EngageNY)

# Multiplying a decimal by a power of 10

Learn to multiply 0.44 times 1000 using powers of 10. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- At0:51how do you get 4.40$?(46 votes)
- Each single stamp costs $0.44. The stamps come in rolls of 1000.

So, you have 1000 stamps, each costing $0.44 each.

If you only wanted 10, multiply 10 x $0.44 to get $4.40 for 10 stamps.

If you want 100, multiply 100 x $0.44 to get $44.00 for 100 stamps.

If you want 1000, multiple 1000 x $0.44 to get $440.00 for 1000 stamps.

Notice, the decimal is "moving" to the RIGHT each time? That's what makes the "multiplication by 10's" so easy! You just move the decimal to the right, one place for every 10 that you're multiplying by.

10 is just 10 (also known as 10^1)

100 is 10 x 10 (also known as 10^2)

1000 is 10 x 10 x 10 (also known as 10^3)

This comes in handy when you're using the metric system.(2 votes)

- do we only move the decimal as many times given?(0 votes)
- as many zeros you multiplying by. ie .55 times 10,000 equals 5,500 the decimal move four times because there four zeros after the 1.(20 votes)

- what if ther is 3000000000000000times10 you gone move that all 0s(6 votes)
- You just add one more 0 to it

so 3000000000000000 times 10 = 3000000000000000 plus one more 0 is equal to 30000000000000000. Sal just shows why we do it.(1 vote)

- explain why is 10/100 less than 8/10(2 votes)
- If you simplify 10/100, you will get 1/10. 1/10 is surely less then 8/10.(5 votes)

- What is the value of 0.6× 0.35(3 votes)
- 6*35=210. move decimal 3 to the left since you have 3 to the right spaces =.21(1 vote)

- does this help you with other lessons(1 vote)
- if you just have 1000x5 how many places do yuo move your decimal point(2 votes)
- Because you can always add as many zeros as you want past the decimal dot, 1000 x 5 is equivalent to 1000 x 5.000 .

Then, you simply move the dot three times to the right, because 1000 is ten to the power of three.

5.000 → 50.00 → 500.0 → 5000

The result is 5000. I hope that helped.(2 votes)

- please give me an every day example of when you would use power

of ten in real life(2 votes)- You bet! Powers of 10 are used all the time in scientific notation. Scientific notation is a way of writing very large or very small numbers. Scientists, engineers, mathematicians and others use this method of writing numbers all the time. You've got to be an expert in "powers of ten" to use scientific notation properly.(1 vote)

- Please give a real life situation when multiplying a decimal by power of , concerning money. Would converting coins (.10) into dollars be a real situation? Thank you(2 votes)
- All right! 1 Chinese Yuan = .15 US dollars. So let's say you are a tourist in Western China's border, and you really want to buy a basket. You have 300 dollars. The basket is 115 Yuan, though. You have to exchange your money into Chinese currency, however. So let's do the math-

300/ .15 = 2000

So you have 2000 Yuan! And converting coins to dollars would be a real life situation, just not on paper. You can do that in your head, hopefully. If you need more help comment!(1 vote)

- So, shifting the decimal number to ylthere left according to the number of zeros in the power of ten is wrong? Ex .10x100(2 votes)
- It is correct, it's the 'Adding zeros to the end' that's wrong(1 vote)

## Video transcript

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.