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Multiplying decimals: place value

Sal uses an understanding of place value to multiply 2.91x3.2. Created by Sal Khan.

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  • duskpin seed style avatar for user Darlene Heard
    At Sal starts talking about the sum being divisible by 1000, but I don't understand why 100 divided by 10 becomes 1000. Can anyone shed any light on this? Thank you
    (26 votes)
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  • sneak peak purple style avatar for user bluebelle567
    Please bear with me, just a dumb kid asking a dumb question. Couldn't you just line up the decimals and multiply like normal? And if not, why?
    (14 votes)
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    • stelly blue style avatar for user Kim Seidel
      Unlike adding/subtracting decimals, lining up the decimal points to multiply the numbers provides no value. It usually causes you to have extra work due to the zeros you put in as placeholder.

      You are better off ignoring the decimal points while you are mulitplying. Multiply as usual. When you are done, then you determine the placement of the decimal point. This is done by adding the number of decimal digits in each original number. It tells you how many decimal digits your answer needs.
      For example: 3.25*1.3
      -- Ignore the decimal points. Multiply 325*13 = 4225
      -- Determine the number of decimal places: 1st number has 2 decimal digits and 2nd number has 1. 2+1 = 3 decimal digits for the answer.
      -- Place the decimal point in your result so that you have 3 decimal places: 4.225

      Hope this helps.
      (14 votes)
  • duskpin sapling style avatar for user kendy.mendozabaltazar
    What is comput?
    (11 votes)
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  • piceratops ultimate style avatar for user CaptainSRT
    Never mind. Why is it so hard to remember it all and do it. Make it much more easier if you want people to be able to learn this
    (10 votes)
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  • duskpin seed style avatar for user arburns3
    Man, this Sal guy is really great! He is the only reason I am passing my super hard math class lol.
    (9 votes)
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  • marcimus purple style avatar for user lahariamirisetti
    Aren't you supposed to place the decimal points? When multiplying?
    (5 votes)
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    • primosaur seed style avatar for user Ian Pulizzotto
      When multiplying decimals, you can first ignore the decimal points and multiply as usual with whole numbers. In the end, place the decimal point to the left by the total number of decimal places in the two decimals being multiplied. In this way, multiplication of decimals differs fundamentally from addition of decimals (which requires aligning the decimal points first before adding).

      Have a blessed, wonderful day!
      (9 votes)
  • orange juice squid orange style avatar for user Ariel Bowers
    So with this concept, I could redo 5.06*75 as 506*75, and later take 37,950.0 (the product of 506*75) and move the decimal over 2 numbers (because I moved it 2 numbers to the right to make it a whole number) to get 279.5?
    Thank you Sal!!
    (7 votes)
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  • primosaur tree style avatar for user BeauB
    do you guys like call of duty warzone
    (6 votes)
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  • leafers tree style avatar for user Zoltan Szabo
    I don't understand the regrouping made by Sal. Why is it 291*32/100/10? For me the logic of rewriting (even though it gives the same result) would be (291*32):(100*10). No?
    (5 votes)
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  • female robot grace style avatar for user Avwa
    I'm so confused with multiplying decimals. I would LOVE some help! please?
    (3 votes)
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    • primosaur seed style avatar for user Ian Pulizzotto
      First just ignore the decimal points and multiply the whole numbers as usual. Then in the end, count the total number of decimal places in the numbers being multiplied, and move the decimal point that many places to the left in your answer.

      Example: let's say you're asked to multiply 6.3 * 0.24.
      First multiply 63 * 24 to get 1512.
      Note that 6.3 has one decimal place, and 0.24 has two decimal places. The total is three decimal places. So move the decimal point three places to the left to get a final answer of 1.512.

      Note that multiplying decimals, unlike adding and subtracting decimals, does not require lining up the decimal points first!

      Have a blessed, wonderful day!
      (4 votes)

Video transcript

Let's see if we can calculate 2.91 times 3.2. 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 2.91 is the same thing as 291 divided by 10. Or not divided by 10, divided by 100. And we know that if you divide something by 100, you are going to move the decimal place two places to the left-- one, two. And you would end up at 2.91. It also make sense, if I take 2, and I multiply it by 100, I'd get 200. Or if I take 200 and divided by 100, I would get 2. So it makes sense that 2.91 is the same thing as 291 divided by 100. Similarlarly-- I can never say that word-- 3.2 can be rewritten. It's the same thing as 32 divided by 10. Now, why is all of this interesting? Well, I could rewrite 2.91 times 3.2 as being the same thing as. Instead of 2.91, I can write 291 divided by 100. And then 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 divided by 100. I'm just reordering this-- divided by 100, divided by 10. Or I could rewrite this. This is equal to 291 times 32. If I divide by 100 and then I divide by 10 again, I'm essentially dividing by 1,000. So this part right over here, I could rewrite as dividing by 1,000. 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 1,000. So let's calculate 291 times 32. Let me write it right over here. 291 times 32. Notice, I've just essentially rewritten this without the decimals. So this right over here-- but of course, these are different quantities than this one is right over here. To go from this product to this product, I have to divide by 1,000. 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-- oh, let me throw a 0 here. Because this isn't a 3. This is now a 30. So 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 notice, it's in the tens place right now. And then 3 times 9 is 27. Carry the 2. 3 times 2 is 6, plus 2 is 8. And now 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 9,312. So this is going to be equal to 9,312 divided by 1,000. And what's this going to be equal to? Well, if we start with 9,312-- and let me throw a decimal there. Dividing by 1,000 is equivalent to moving the decimal over three places to the left. So you divide by 10, divide by 100, divide by 1,000. So that's going to be 9.312. So if you divide by 1,000, you will get to 9.312. Let me write the decimal in purple. 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 re-expressed this as 291 divided by 100. And this is 32 divided by 10. Dividing by 100 and dividing by 10-- this essentially accounts for these three decimal places. So we essentially get rid of those decimal places. But then we have to reintroduce those three decimal places by dividing. Or we have to shift-- here we shift the decimal an aggregate to the right three times-- one, two, and then three. Now, in order to make sure we get the right product, we've 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. We essentially, to 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 1,000, if you think about both of these. And so now we have to divide by 1,000 to get the right value. So that's why three spaces to the right of the decimal here, three digits to the right of the decimal here.