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# Intro to multiplying decimals

## Video transcript

let's see if we can multiply nine times zero point six nine times zero point six or another way to write it we want to calculate nine times zero point six I'll write it like this zero point six 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 0.6 is the same thing as 6 divided by 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're moving the decimal one place to the left so I'm assuming you've 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 as 9 times 0.6 is 6 divided by divided by 10 and this expression right over here we could either do the 6/10 first in which case we would get to 0.6 and this would it 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's all about just moving the decimal place so we could write 9 9 times 6 9 times 6 we already know is 54 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 is 10 to the place it represents 10 times as much as the place to that's right or each place represents one tenth of the place to the left so 54 divided by 10 this is going to be you could start with 54 54 and I'll put a zero 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 five point four and that should make sense to you five times ten is fifty point four times ten is four so it makes sense that 54 divided by 10 54 divided say equalize I'd write 54 divided by 10 is equal to five point four so this right over here is equal to five point four and that's what this is this is equal to five point four notice 9 times 6 is 54 9 times zero point six is five point four 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 products let's say I ignored the decimal I just said nine times six I would've gotten 54 but then I had to divide by 10 in order to take account of the decimal take account of the fact that this wasn't a six this was a six tense and so I have one number to the right of the decimal here and I want you to think about 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 the right of the decimal I'll let you think about that