How to Do Addition & Subtraction in Exponential Notation

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Doing addition and subtraction in exponential notation is also known as scientific notation. Do addition and subtraction in exponential notation with help from an experienced mathematics educator in this free video clip.

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Video Transcript

Hi, my name's Marija. And today, I'm going to show you how to do addition and subtraction in exponential notation. Exponential notation is also known as scientific notation. And if I had two numbers that were written in scientific notation, such five times 10 to the third. And I wanted to add that to let's say, six times 10 to the second. I can't add them quite yet. So, when you're adding numbers that are in the exponential notation, they have to have the same exponent. So, we're going to have to change one of these terms in order to have the exponent of three in both of them or two in both of them. So, I'm going to go ahead and change the five, this, maybe I'll change the five times 10 to the third. And then, we'll show you the other one. So, if I want the 10 to the third to become 10 to the second. What I did was, I moved the three to the left. So, to balance that out, I'm going to have to move the decimal in the five to the right. So, this is actually going to become 50 times 10 to the second power. Now, I have 50 times 10 to the second power plus six times 10 to the second power. And because they have the same exponent, I can add them. So, I add the front two numbers, the 50 and the six and I get 56. And I keep the 10 to the second power. Now, I'm not done because the result is not in scientific notation. So, what I have to do now, is rewrite this. So, the 56, I need to move this decimal back one space, so that it becomes five point six. So, in scientific notation, your first number's always between zero and 10, so I can't have 56. Now, because I move the decimal to the left, I'm going to have to move the exponent to the right and make this to the third. So this is going to become five point six times 10 to the third. The other way that I could have done this, would have been to make the six have an exponent of three with its base of 10. So,if I'm going to move the two to a three, I have to make the six, a point six. I'm going to add five and point six, I would still end up with the same answer that I just got. And that's how you add and subtract numbers that are in exponential notation.

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