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# Multiplying decimals: place value

## Video transcript

let's see if we can calculate two point nine one times three point two and I encourage you to pause this video and try it out on your own so the way I'm going to think about it is two point nine one two point nine one is the same thing as 291 divided by ten and we know that when you or not divided by ten divided by 100 and we know that if you divide something by 100 you're going to move the decimal place two places to the left one two and you would end up at two point nine one it also makes sense if I take two and I multiply it by a hundred I'd get two hundred or if I take two hundred and divided by a hundred I would get two so it makes sense that two point nine one is the same thing as two hundred ninety-one divided by one hundred similarly I can never say that word 3.2 can be rewritten it's the same thing as 32 divided by 32 divided by ten now why is all of this interesting well I could rewrite two point nine one times three point two I can rewrite two point nine one times three point two times three point two as being the same thing as instead of two point nine one I can write 291 divided by 100 291 divided by 100 and then x times instead of writing 3.2 I could write 32 divided by 10 and this can be rewritten as this is going to be equal to 291 times 32 times 32 times 32 divided by a hundred divided by 100 I'm just reordering this divided by 100 divided by 10 divided by 10 or I could rewrite this as I could rewrite this this is equal to 291 times 32 times 32 if I divide by a hundred and then I divide by 10 again I'm essentially dividing by a thousand so this part right over here I could rewrite as dividing by a thousand now why is this interesting well I already know how to multiply 291 times 32 and then we know how to move the decimal so that when we divide by a thousand so let's calculate 291 times 32 let me write it right over here 291 times 32 times 32 notice this I've just essentially rewritten this without the decimals so this right over here but of course these are different quantities and this one is right over here to go from this product to this product I have to divide by a thousand but let's just think about this we already know how to compute this type of thing 2 times 1 is 2 2 times 9 is 18 carry the 1 2 times 2 is 4 plus 1 is 5 and now we can think about the 3 3 times 1 I'll actually let me throw a 0 here because this is now this isn't a 3 this is now a 30s this is in the tens place so that's why I put a 0 there so 30 times 1 is 30 that's why we say 3 times 1 is 3 but it's notice it's in the tens place right now and then 3 times 7 so 3 times 9 is 27 carry the 2 3 times 2 is 3 times 2 is 6 plus 2 is 8 and now we can add we can add and we would get 2 8 plus 3 is 11 6 plus 3 is 13 and then you get 9 so you get nine thousand three hundred and twelve so this is going to be equal to nine thousand three hundred and twelve divided by 1,000 divided by 1000 and what's this going to be equal to well if we start with nine thousand three hundred and twelve and I throw a decimal there dividing by a thousand is equivalent to moving the decimal over three places to the left so you divide by 10 divided by 100 divided by a thousand so that's going to be nine point three one two so if you if you divide by 1,000 you will get to nine point three one two right this nine point three let me write the decimal in purple point three one nine point three one two now there's something very interesting here in our original when we wrote the expression we had one two three total numbers behind the decimal and then over here we have one two three total numbers to the right of the decimal why is this well let's think about it we aree expressed this we express this as 291 divided by hundred and this is 32 divided by 10 the hundred dividing by 100 and dividing by ten this essentially accounts for these three decimal places so we essentially get rid of those three decimal places but then we have to reintroduce those three decimal places by dividing or we have to shift here we shift the decimal and aggregate to the right three times one two and then three now in order to make sure we get the right product we got to shift it back to the left so we're shifting it one two three so we went from this to this for the whole product it was like multiplying it was like dividing by it was we essentially we essentially to go from two go from here to here we multiplied by 100 to go from here to here we multiplied by 10 so in aggregate we multiplied by a thousand and if you think about both of these and so now we have to divide by a thousand to get the right value so that's why three decimal places to the three numbers to three spaces to the right of the decimal here three digits to the right of the decimal here