Scientific Notation Adding and Subtracting

I know. It's so easy. 6.2. Plus 3.1. Equals 9.3. And that's my answer. 9.3 times ten to the third milliliters. The ten to the third states the same. In order to add or subtract and scientific notation you must have the same exponent on both tens. It's like when you're doing fractions. They have to have the common denominator. Here you have to have a common exponent. The same is true with subtraction. As long as these two have the same exponent, we just do 9.5 -5.2 to give us 4.3. Times ten to the 7th, as easy as that. But you ask, what if you don't have the same exponent? For instance, here, this one is raised to the fourth, and this one is raised to the third. Our rule says we can't add them like this. It's okay. I'll help you. 

In order to add them, they have to have the same exponent. So I have a choice. I can add one to this to make it four, or I can subtract one from here to make it three. Either one is fine. Um, let's see. I think I'm going to subtract one. I don't have a very good reason. I just feel like subtracting one. Well, the exponent is easy. It's now ten to the third. And this did the same. But I can't just rewrite this number. If I subtracted one here, Lars tells us that if we subtract we have to move right. And because I subtracted one, I have to move right one. My new number is 50 two times ten to the third. Now they have the same exponent. They are both raised to the third power. I can add them 52 plus 4.2 is 50 6 point two times ten to the third. But you might be asking yourself so this is not a number between one and ten. You would be right self. 

So we need to fix it. We can't leave this as scientific notation because scientific notation has to have a number between one and ten. So we need to move our decimal one to the left. If I move it to the left one, Lars tells us that means add one. We get 5 point 6 two times ten to the fourth as our answer. Let's look at another one. Again, these don't have the same exponent. So I'm going to have to either subtract one from four. Or add one to three. Well, last time we subtracted one from four. So this time, let's add one to three. Our 2.5 times ten to the fourth save the same. Because we want that fourth as our excellent. Plus, something times ten to the fourth. Well, if we add one, wires tells us that if we add, we have to go left left. So we go left. One. .13. Times ten to the fourth. Now I can add them together 2.5 plus .13, and I get 2.63 times ten to the fourth. 

This time, I do have a number between one and ten, so that is my answer. I do not have to change anything. One last example before you're on your own, we check to see that we have the same exponents and we find that we do not. They have to be the same. I'm going to add two to this exponent to make it a 7. The left side says the same minus something times ten to the 7th. Lars tells us that if we add, we have to go left. We added two, so we have to go left two. Point zero two. Now I can add. I check to make sure that the first number is a number between one and ten. It is so that is my answer. I'm not going to go through this whole problem, but I want you to notice that the negative three and the two are not the same. The rules still apply. This time I'm going to have to add 5 to make them the same. Do these 6 problems. If you need a reminder, here is your reminder. Make the two numbers have the same exponent, add the whole numbers, rewrite with the same power, and I would check for a number between one and ten.