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### Course: Pre-algebra > Unit 11

Lesson 7: Arithmetic with numbers in scientific notation- Multiplying & dividing in scientific notation
- Multiplying three numbers in scientific notation
- Multiplying & dividing in scientific notation
- Subtracting in scientific notation
- Adding & subtracting in scientific notation
- Simplifying in scientific notation challenge

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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).

## Want to join the conversation?

- In this video, I still don't understand the concept of this. Please answer, because I don't know what to do(25 votes)
- 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:)(62 votes)

- I am again, just a bit khanfused(28 votes)
- lmao thats really funny(10 votes)

- late at night homework is fun if you watch the videos but why is it fun(14 votes)
- ...because the videos help make the homework easier! The human brain is designed to have fun working with easy stuff that once wasn't easy!(29 votes)

- at3:50, why does he divide by 10?(12 votes)
- You Cannot have a scientific notation over 10 so he divides 38.4 by 10 to make it valid for a scientific notation, giving you the answer of 3.84 x 10^-2(10 votes)

- 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?(12 votes)
- When adding and subtracting scientific notations, how can you tell which side to convert?(6 votes)
- I Don't understand why Sal made the exponents equivalent instead of just subtracting them? I'm not sure I entirely understand this concept(6 votes)
- I don't understand what Sal does to the 4.1 x 10^-2.(6 votes)
- basicaly sal divided 4.1 by 10^2(0 votes)

- 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.(4 votes)
- 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.(4 votes)

- 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)
- 8.41*10^5=841000

7.9*10^6=7900000

841000-7900000=-7059000

7059000=7.059*10^-6

So your answer was correct. It is false.(5 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.