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Multiplying & dividing in scientific notation

Learn how to simplify a multiplication and division expression using scientific notation. The expression in this problem is (7 * 10^5) / ((2 * 10^-2)(2.5 * 10^9)). Created by Sal Khan.

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  • blobby green style avatar for user 00029570
    I need help how did you get 5 from 2 x 2.5 on my calculator i got 4.5
    (0 votes)
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  • piceratops ultimate style avatar for user Gabrielle Burdge
    Does the first factor in the answer need to have a decimal point in it always? Or are there exceptions for problems where if you simplify them another way, the first digit ends up being zero? My question isn't specific to this video, just a general question on this topic.
    (4 votes)
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    • stelly blue style avatar for user Kim Seidel
      The format for scientific notation is that there will always be just 1 digit to the left of the decimal point and that digit can not be zero.
      For example:
      9,300,000 becomes 9.3 x 10^6
      0.0005 becomes 5 x 10^(-4)
      Hope this helps.
      (18 votes)
  • blobby green style avatar for user tennadissing
    Is there a reason why one puts the point right after the first significant figure when using scientific notation? E.g. 245324.321 as 2.45324321*10^5 instead of 245.324321*10^3? I think the last notation is smarter because it is easier to see that the number is a thousand-something.
    (5 votes)
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  • leaf red style avatar for user jonathan1137
    At , Sal says that his fraction can be viewed as 7/5 * 10^5/10^7. Is there any section or video where I can learn the things that fractions can do and how to work well with them?
    (3 votes)
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  • starky sapling style avatar for user Oakley Gatewood
    What do I do if the product/quotient is not appropriate for scientific notation? For example (5.0 x 10^1) x (2.0 x 10^1) which I imagine equals 10 x 10^2. If I had to guess I'd say increase 10^2 to 10^3 and make 10 to 1.0 so that it'd be 1.0 x 10^3. Sorry for any poor wording
    (4 votes)
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  • aqualine ultimate style avatar for user Hassan.S.Karim
    At to , I wish he would have wrote out the 10^5-10^7 to show what he did in his head.
    (5 votes)
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  • blobby green style avatar for user collinsmits999
    Can you subtract exponents if the base is not the same?
    (3 votes)
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  • hopper jumping style avatar for user Markarino /TEE/DGPE-PI1   #Evaluate
    Did Sal make an error here? At , he is checking to see if 1.4 * 10^-2 is expressed in scientific notation. After confirming that 1.4 is greater than or equal to one, he next asks if it is less than or equal to nine.

    But the rule for scientific notation is that the decimal portion of the number must be less than (and not equal to ) 10. If I wrote a number like 9.9 * 10^-2, this would be a decimal that is not less than or equal to nine, but it would be in scientific notation, because the rule is that the decimal must be greater than or equal to one and less than 10.
    (3 votes)
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  • starky tree style avatar for user joaoavocado
    I hate this I put the answer as 4 in one of the questions and it said it was wrong. It said the correct answer was something else that was equal to 4.
    (3 votes)
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    • stelly blue style avatar for user Kim Seidel
      If you post the actual problem, them someone could help you. Without the details its hard to say what was wrong.

      Did you look at the hints? I find them useful if something is marked wrong and I think I have the correct value. If you really think the website has an error, you need to use the "report a problem" link within the exercise set.
      (3 votes)
  • eggleston blue style avatar for user thiccboy
    I get the multiplication, but the division looks like common core. 😳😔😫😡
    (4 votes)
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Video transcript

We have 7 times 10 to the fifth over 2 times 10 to the negative 2 times 2.5 times 10 to the ninth. So let's try to simplify this a little bit. And I'll start off by trying to simplify this denominator here. So the numerator's just 7 times 10 to the fifth. And the denominator, I just have a bunch of numbers that are being multiplied times each other. So I can do it in any order. So let me swap the order. So I'm going to do over 2 times 2.5 times 10 to the negative 2 times 10 to the ninth. And this is going to be equal to-- so the numerator I haven't changed yet-- 7 times 10 to the fifth over-- and here in the denominator, 2 times-- let me do this in a new color now. 2 times 2.5 is 5. And then 10 to the negative 2 times 10 to the ninth, when you multiply two numbers that are being raised to exponents and have the exact same base-- so it's 10 to the negative 2 times 10 to the negative 9-- we can add the exponents. So this is going to be 10 to the 9 minus 2, or 10 to the seventh. So times 10 to the seventh. And now we can view this as being equal to 7 over 5 times 10 to the fifth over 10 to the seventh. Let me do that in that orange color to keep track of the colors. 10 to the seventh. Now, what is 7 divided by 5? 7 divided by 5 is equal to-- let's see, it's 1 and 2/5, or 1.4. So I'll just write it as 1.4. And then 10 to the fifth divided by 10 to the seventh. So that's going to be the same thing as-- and there's two ways to view this. You could view this as 10 to the fifth times 10 to the negative 7. You add the exponents. You get 10 to the negative 2. Or you say, hey, look, I'm dividing this by this. We have the same base. We can subtract exponents. So it's going to be 10 to the 5 minus 7, which is 10 to the negative 2. So this part right over here is going to simplify to times 10 to the negative 2. Now, are we done? Have we written what we have here in scientific notation? It looks like we have. This value right over here is greater than or equal to 1, but it is less than or equal to 9. It's a digit between 1 and 9, including 1 and 9. And it's being multiplied by 10 to some power. So it looks like we're done. This simplified to 1.4 times 10 to the negative 2.