Arithmetic with numbers in scientific notation
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- [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.