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# Decimal multiplication place value

CCSS.Math:

When we rewrite decimal multiplication using fractions, we can use the commutative and associative properties of multiplication to justify how we place the decimal point in the standard multiplication algorithm. Created by Sal Khan.

## Want to join the conversation?

- how did you know all of this(7 votes)
- Sal big brain(3 votes)

- Isn't their an easier way to multiply decimals?(7 votes)
- yes there is at around3:25he tells you(1 vote)

- you can desplede your badges that you earn(6 votes)
- I had to skip from 6th to 8th grade and I got this problem for homework but I don't understand it (a+b)(a2+b2)(a3+b3)(a4+b4)(c+d)(c2+d2)(c3+d3)(c4+d4)=1=9=7=25(1)(2)(3)(4)

First I used the identity

(a2+b2)(c2+d2)=(ac−bd)2+(bc+ad)2

Use this identity to (4) too and simplify (3), we obtain

(a2+b2−ab)(c2+d2−cd)=7

And suppose x=abcd use ac=x/bd,bc=x/ad But then I got stuck... at10:28am(4 votes)- bruh wat da hail is dat(1 vote)

- his full name is Abdul Rashid Salim Salman Khan(4 votes)
- Ik this is random but did anybody know that Salman khan (sal) is a famous hindu actor?(2 votes)
- No I did not cool fact(2 votes)

- Wouldn't the answer be 0.04575? BC that would be equal to the ten thousands column in decimals. Maybe I am wrong?🤷♀️🤷♀️🤷♀️(2 votes)
- vhfry f h hy tty ht yty rj h(3 votes)

- I had to skip from 6th to 8th grade and I got this problem for homework but I don't understand it (a+b)(a2+b2)(a3+b3)(a4+b4)(c+d)(c2+d2)(c3+d3)(c4+d4)=1=9=7=25(1)(2)(3)(4)

First I used the identity

(a2+b2)(c2+d2)=(ac−bd)2+(bc+ad)2

Use this identity to (4) too and simplify (3), we obtain

(a2+b2−ab)(c2+d2−cd)=7

And suppose x=abcd use ac=x/bd,bc=x/ad But then I got stuck...(2 votes) - 667587483*37635267533.9867(1 vote)
- If you paus and then after 2 or 3 sec. unpaus, you'll get more energy points!(1 vote)

## Video transcript

- [Instructor] This is an
exercise from Khan Academy. It tells us that the product 75 times 61 is equal to 4,575. Use a previous fact to
evaluate as a decimal. This right over here, 7.5 times 0.061. Pause this video and see
if you can have a go at it. All right, now let's do this together. So the first thing that you might realize is that 7.5 is the same thing as 75 divided by 10. And 0.061, this is 61 thousandths. This right over here
is the same thing as 61 divided by 1,000 and we're gonna take the
product of these two things. Another way we could write this, 75 divided by 10, this is the same thing as 75 over 10 and I'm gonna take the product of that, and 61 thousandths, 61 divided by 1,000. So that would be 61/1,000. Now, when we look at it, either of these ways, well actually, I'll do both
of them at the same time. You could change the order of the multiplication
and the division here. So you could start with 75 times 61, 75 times 61, and then divide that by 10, and then divide that by 1,000. You could do it that way or you could look right over here and say, all right, if I'm taking this product, my numerator is going to be 75 times 61, 75 times 61. And then, my denominator is going to be 10 times 1,000 which is essentially the same thing as dividing by 10, and then dividing by 1,000. And of course, that is going to be 10,000. Now on the left-hand
side, right over here, they told us what this is, it's 4,575. So it's 4,575 divided by 10, and then divided by 1,000. Well, if I divide by 10, and then I divide by 1,000, that's equivalent to dividing by 10,000. This is dividing by 10,000 and you could see that over here. We're dividing by 10,000 as well right over here. And the 75 times 61, this is 4,575. Now they want us to
evaluate it as a decimal. We've now expressed it as a fraction and I still haven't
fully evaluated this yet. So we really wanna think about this as 4,575 ten thousandths and you can see that very explicitly here. There's 4,575 ten thousandths. So how do we write that? Well, if I have a decimal right over here, that's the tenths place. This is the hundredths, thousandths, ten-thousandths place. So we have this many ten thousandths, 4,575 ten thousandths and we're done. So this is gonna be 0.4575. Now I know what some of
you might be thinking. Hey, I learned a technique where if I'm taking the
product of two numbers, I could take the product
of those two numbers, or if I'm taking the
product of two numbers that are decimals, I could remove the decimals
from them essentially, take their product which they actually
gave us right over here. And then, count how
many digits to the right of the decimal there were
in our original numbers. So we have one, two, three, four digits to the right of the decimal. And so what I do is I then move, I then make sure that there's four digits to the right of the
decimal in the product. And so I would say, okay, one, two, three, four, that looks good and I've gotten the same answer a lot faster than we just did it. Well, whole reason why I
just did it the way I did is to show you why that works. When we take the product
of the two numbers without the decimals, we're essentially ignoring the fact that the original product
was dividing by 10 and dividing by 1,000, and that's because we had one digit behind to the right of the decimal here, and we had three digits to the
right of the decimal there. And so later after we take the product, we have to go and then
actually take that product and divide by 10, and divide by 1,000 or divide by 10,000. So that's why you can then
just say, all right, well now, we originally had four
digits to the right, so we still have to have four digits to the right of the decimal point.