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# Intro to multiplying decimals

Sal introduces multiplying decimals with problems like 9x0.6. Created by Sal Khan.

Video transcript

Let's see if we can
multiply 9 times 0.6. Or another way to write it, we
want to calculate 9 times 0.6. I'll write it like this-- 0.6. We want to figure out
what this is equal to. And I encourage you
to pause the video and try to figure
it out on your own. And I'll give you a
little bit of a hint. 0.6 is the same thing
as 6 divided by 10. We know that if we start with
6, which we could write as 6.0, and if you were to divide
it by 10, dividing by 10 is equivalent to moving
the decimal place one place to the left. So 6 divided by 10 is 0.6. We are moving the decimal
one place to the left. So I'm assuming you
given a go at it. But what I'm going
to do is use this that we already know to rewrite
what we're trying to multiply. So 9 times 0.6 is the
same thing is 9 times-- 0.6 is 6 divided by 10. And this expression
right over here, we could either do the 6 divided
by 10 first, in which case we would get 0.6, and this
would turn into this problem. Or we could do the
9 times 6 first. And so let's do 9 times 6,
which we know how to calculate, and then divide by 10, which
we also know how to do. That. all about just moving
the decimal place. So we could write 9 times 6. 9 times 6, we
already know, is 54. I'll do that in orange--
is going to be 54. So this right over here is 54. And now to get to
this expression, we have to divide by 10. We have to divide by 10. And what happens when we
divide something by 10? And we've seen this in previous
videos, why this is the case. This is all about what
decimal notation means. Each place represents 10
times as much as the place to its right, or each place
represents 1/10 of the place to the left. So 54 divided by
10, this is going to be-- you could start with 54. And I'll put a 0 here
after the decimal. And when you divide
by 10, that's equivalent of shifting the
decimal one to the left. This is going to
be equal to 5.4. And that should
make sense to you. 5 times 10 is 50. 0.4 times 10 is 4. So it makes sense that
54 divided by 10-- I shouldn't say equal. I'd write 54 divided
by 10 is equal to 5.4. So this right over
here is equal to 5.4, and that's what this is. This is equal to 5.4. Notice, 9 times 6 is 54. 9 times 0.6 is 5.4. Now you might see a
little pattern here. Between these two numbers,
I had exactly one number to the right of the decimal. When I take its product, let's
say I ignored the decimal. I just said 9 times 6,
I would've gotten 54. But then I have to
divide by 10 in order to take account of
the decimal, take account of the fact
this wasn't a 6. This was a 6/10. And so I have one number to
the right of the decimal here. And I want to you
to think about that whether that's a
general principle. Can we just count the
total numbers of digits to the right of the
decimals and then our product is going to have
the same number of digits to right of the decimal? I'll let you to
think about that.