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# Intro to multiplying decimals

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

## Want to join the conversation?

- how can you multiply 9 by 0.6, sure, 0.6 is in the tens but its only a fraction of a number...(8 votes)
- boston kailey, you can turn 9 and 0.6 into fractions, then solve them that way, after that you might need to turn it back into a decimal depending on the certain question. Hope this helps!! :)(2 votes)

- I am starting grade 6 but what does BIDMAS stand for and mean(12 votes)
- BIDMAS is another way to express the order of operation. It stands for the following: Brackets (Parentheses), Indices (Exponents), Division, Multiplication, Addition, and Subtraction. But PEMDAS is also correct.(2 votes)

- Yes. 9 x 0.5 = 4.5

Good job!(0 votes)

- Just write it down, don't try to do it in your head.(8 votes)
- yes you are indeed correct(3 votes)

- I'm in 4th grade and in already know about decimals(6 votes)
- Emotional grammar break down(4 votes)

- at2:40why cna you just count how many times it goes left(7 votes)
- His voice is so much deeper! love you sal!! your my hero!! ive learned so much from you!!(6 votes)
- Okay. Sal's our definate learning hero, ha!(1 vote)

*I'm confused can you help me? pretty please*(2 votes)- Audrey what are you confused with? All your doing is multiplying then moving the place-

here's an example:

5x 0.2 now that looks hard right? Now to make it easy to make the 0.2 a two, so now ask yourself what is 5x2? Well, that's easy! It's ten! Now all you have to do is divide ten by 10. In other words, you must move the decimal left one time. So you have 10.0, what's your answer once you move the decimal (don't forget the decimal is that tiny dot between the numbers!) moving the decimal is just moving the dot. So since we have 10.0, what happens when you move the decimal to the left once? You get 1.00! That would be your answer, so you understand more if you had 0.02 instead of 0.2, then you would move the decimal two times to the left because there are two numbers to the right of the decimal. If you had 0.002, then you would move the decimal three times to the left and so on.

I hoped this helped! If you are still confused, then tell me and/or watch another video!(8 votes)

- I still don't really understand. Can you please re explain it more detailed?(3 votes)
- The key to this is the concept that you can divide or multiply anything by 1 without changing the number. So: the problem is 3.5/1.2. Okay, we're going to multiply that by 1. 10/10=1, right? So we can totally multiply 3.5/1.2 by 10/10. You get

3.5/1.2 = 3.5/1.2 x 10/10 = 3.5 x 10/1.2 x 10 = 35/12. Then you go divide those whole numbers. You didn't actually change the problem, since you only multiplied by 1, you just made it easier!(5 votes)

- I am confused, can someone help me?

I don't get the way that Sal does it.

Thanks.(4 votes)- who is Sal? is he the person in the video.(2 votes)

## 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.