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Subtracting in scientific notation

Learn how to subtract numbers written in scientific notation. The problem solved in this video is (4.1 * 10^-2) - (2.6 * 10^-3).

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  • blobby green style avatar for user gabking100
    In this video, I still don't understand the concept of this. Please answer, because I don't know what to do
    (14 votes)
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    • duskpin ultimate style avatar for user Tay9404
      Hello:)
      So I have replied to other students questions, and when Sal asked us to pause and solve on our own, I ended up solving differently than what he had us do. Now, this may be an exception, but Ii believe we can use this method as well. It may depend on the question, but maybe this will make it simpler to understand.
      Step (1) Solve the problem 4.1 * 10^-2. Okay, so move the decimal to the left two times. 0.041.
      Step (2) Solve the second problem 2.6 * 10^-3. Okay, so move the decimal to the left three spaces. 0.0026
      Step (3) Subtract 0.0026 from 0.041
      0.0410 <---(You have to add a zero in order to
      0.0026 subtract. Or you could always do it in
      ------ your head:)
      0.0384
      Step (4) Turn into Scientific Notation~ you have to move the decimal over to the right two times in order for it to become a scientific notation. So you would write 3.84 * 10^-2, and the exponent is negative because in order for you to go back to the original answer, you would have to move the decimal two times to the left. Whenever you move the decimal to the left, the exponent is going to be negative.
      There ya go! Another way to solve for these kinds of problems :) I hope this helped you and anyone else who was confused. If I made any mistake or anyone has any comments or questions, just let me know. I love to hear your feedback:)
      (37 votes)
  • duskpin tree style avatar for user zirinart_lapus
    late at night homework is fun if you watch the videos but why is it fun
    (8 votes)
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  • piceratops seed style avatar for user chloe moody
    at , why does he divide by 10?
    (7 votes)
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  • leafers ultimate style avatar for user dooboo451
    I have a question. Why Can't You Just Use a big number like 676 and multiply it by 10 to the power of 3 to express 676, 000? Why is it that we need to express it as 6.76 multiplied by 10 to the power of 5? Isn't it the same thing? If we had a random long number like 162537901468 then it would be a long and complicated decimal... Why can't we just express it as 162 times 10 to the power of 9 just approximately instead of writing a looooong and confusing decimal?
    (8 votes)
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  • blobby green style avatar for user alexterissa
    I don't understand what Sal does to the 4.1 x 10^-2.
    (5 votes)
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  • blobby green style avatar for user Nancy Bates Pearson
    What do you do when one exponent is negative and one positive
    (4 votes)
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  • aqualine ultimate style avatar for user evismiyamoto
    I'm a little confused... I was doing the Practice and I don't think Sal explains which number we have to multiply and divide. For example, 4.2*10^-3 + 2.9*10^-4. I don't which one I should be multiplying snd dividing.
    (3 votes)
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    • primosaur seed style avatar for user Ian Pulizzotto
      This can be done with either part, as long as the exponents are made the same. Once the exponents are made the same, we can add (or subtract) the numbers that multiply the common power of 10, keep the common power of 10, then convert to scientific notation in the end.

      For your example, 4.2*10^-3 + 2.9*10^-4, you could use 42*10^-4 + 2.9*10^-4 for the first step, or use 4.2*10^-3 + 0.29*10^-3 for the first step. Either will give the same result in the end, because 44.9*10^-4 is equivalent to 4.49*10^-3.
      (3 votes)
  • blobby green style avatar for user 06SChapman
    I'm a little confused for my hw it says (8.41 x 10^5)-(7.9 x 10^6) equals -7.14 x 10^6 is it true or false . I said it was false and my friend said it was true I need help.
    (3 votes)
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  • aqualine seedling style avatar for user bjkwestvalley
    So the first step (when you make the 4.1 into 41 and 10-2 to 10-3) which side do you know to convert? Like how do I know if I am suppose to convert the 10-3 to 10-2 or the 10-2 to 10-3? Because converting which side makes a big difference in the answer...
    (3 votes)
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    • mr pink green style avatar for user David Severin
      It should not make any difference in the answer.
      converting 41x10^-3 - 2.6x10^-3 gives 38.4x10-3 and moving the decimal back gives 3.84x10-2.
      Doing it the other way moves the decimal of 2.6 to the left, so you have 4.1x10^-2 - .26x10_2 =3.84x10^-2.
      (2 votes)
  • piceratops sapling style avatar for user PiperR
    Hello. I know basic scientific notation rules, but I cannot find anything on how to add scientific notation. Please help!
    (2 votes)
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    • female robot ada style avatar for user Angelica Chen
      When you add in scientific notation, all you need to do is make sure both the exponents are the same, or change them so they are the same. Then add the main number, keeping the exponents how they are. Example:

      3.14•10^12 + 2.67•10^11
      The exponents must be the same, so I'll convert 2.67•10^11 into 0.267•10^12.

      3.14•10^12 + 0.267•10^12 =
      3.407•10^12
      (4 votes)

Video transcript

- [Voiceover] What I want to do in this video is get a little bit of practice subtracting in scientific notation. So let's say that I have 4.1 x 10 to the -2 power. 4.1 x 10 to the -2 power and from that I want to subtract, I want to subtract 2.6, 2.6 x 10 to the -3 power. Like always, I encourage you to pause this video and see if you can solve this on your own and then we could work through it together. All right, I'm assuming you've had a go it. So the easiest thing that I can think of doing is try to convert one of these numbers so that it has the same, it's being multiplied by the same power of ten as the other one. What I could think about doing, well can we express 4.1 times 10 to the -2? Can we express it as something times 10 to the -3? So we have 4.1 times 10 to the -2. Well if we want 10 to the -2 to go to 10 to the -3 we would divide by 10, but we can't just divide by 10. That would literally change the value of the number. In order to not change it, we want to multiply by 10 as well. So we're multiplying by 10 and dividing by 10. I could have written it like this. I could have written 10/10 times, let me write this a little bit neater. I could have written 10/10 x this and then you take 10 x 4.1, you get 41, and then 10 to the -2 divided by 10 is going to be 10 to the -3. So this right over here, this is equal to 10 x 4.1 is 41 times 10 to the -3. And that makes sense. 41 thousandths is the same thing as 4.1 hundredths and all we did is we multiplied this times 10 and we divided this times 10. So let's rewrite this. We can rewrite it now as 41 X 10 to the -3 minus 2.6, -2.6 x 10 to the -3. So now we have two things. We have 41 X 10 to the -3 - 2.6 x 10 to the -3. Well this is going to be the same thing as 41 - 2.6. - 2.6, let me do it in that same color. That was purple. - 2.6, 10 to the -3. 10, whoops, 10 to the -3. There's 10 to the -3 there, 10 to the -3 there. One way to think about it, I have just factored out a 10 to the -3. Now what's 41 - 2.6? Well 41 - 2 is 39, and then -.6 is going to be 38.4. 38.4 and then you're going to have times 10 to the -3 power. x 10 to the -3 power. Now, this is what the product, or this is what the difference of these two numbers is but this is no longer in scientific notation. In order to be scientific notation this number right over here has to be between 1, has to be greater than or equal to 1 and less than 10. So what we could do is we could divide this number right over here by 10. We can divide this by 10 and then we can multiply, then we can multi...so we could do this. We could, kind of the opposite of what we did up here. We could divide this by 10 and then multiply by 10. So if you divide by 10 and multiply by 10 you're not changing the value. So 38.4 divided by 10 is 3.84 and then all of this business, 10 to the -3, 10 to the -3 x 10 is 10 to the -2 power. So this is going to be 3.84 x 10 to the -2 power.