6 Easy Steps for Adding and Subtracting in Scientific Notation

Here’s How to Add and Subtract in Scientific Notation

Completing any Add and Subtract in Scientific Notation Example Problem

When Adding and Subtracting in Scientific Notation the powers of the numbers you are adding or subtracting must be equivalent. In the event that they are equivalent, you can simply combine the coefficients together. If the powers are not equivalent, you should make them equivalent by moving one of the decimals so that the powers will become equivalent. Once the powers are equivalent you can either add the coefficients for adding scientific notation or subtracting the coefficients for subtracting scientific notation. The last step for Adding and Subtracting in Scientific Notation is to check that the coefficient is somewhere in the range of 1 and 10. This is the easiest way for solving how to add and subtract scientific notation.

Watch the Explanation of Adding and Subtracting in Scientific Notation Video

Watch our free video on how to solve Adding and Subtracting in Scientific Notation. This video shows how to add scientific notation and how to subtract scientific notation. You can also try some practice problems that are on our free Adding and Subtracting Scientific Notation worksheet that you can get by submitting your email above.

Watch the free Adding and Subtracting in Scientific Notation video on YouTube here: Adding and Subtracting in Scientific Notation

Video Transcript:

This video is about adding and subtracting in scientific notation. You can get the scientific notation addition and subtraction worksheet we use in this video for free by clicking on the link in the description below. Watch this video to find out how to add and subtract scientific notation.

The first problem we’re going to use to show you adding and subtracting scientific notation gives us 9 times 10 to the 9th minus 2 times 10 to the 9th. When adding or subtracting in scientific notation you are going to take the coefficients of each number that is being added or subtracted and you are going to either add or subtract those two together. In this case we have a 9 and a 2  these will be what we eventually will add or subtract together. The second part of adding or subtracting a scientific notation that you need to be aware of is that our powers of 10 must be equal. In other words the exponent on the power of 10 must be the same. For example, if this was, let’s say 10 to the seventh power, we could not subtract these because this exponent is 9 and this exponent is 7. We would have to change the 7 into a 9 and once it was a 9 then we could add or subtract, but in the case of our first example we have exponents that match.

So we’re going to go ahead and solve this problem. When solving this we will take our coefficients which is 9 and 2 and we’re going to subtract them from each other, then we’re going to rewrite our power of 10 right next to it. We will do times 10 to the 9th power, when adding or subtracting the power of 10 has to be equal. Once the exponent is equal you will keep the exponent the same in your answer. The next step is to actually go ahead and subtract the coefficient. 9 minus 2 is 7 and then we will rewrite times and then our power of 10 which is 10 to the 9th power. So our answer in scientific notation is 7 times 10 to the 9th power because we do not change the power of 10 in our answer.

Number 2 is very similar to number 1. This problem will show you how to add scientific notation with different exponents. We’re given 3 six times ten to the seven plus two point one times ten to the seventh. We know we’re adding now we’re going to add our coefficients together which is three point six plus two point one. We’re going to go ahead and write that three point six plus two point one. Now if you look at our power of 10 our exponent is the same for each power of 10. 10 to the seventh here and ten to the seventh here. We do not have to change the exponent on the power of 10 because it is already equal, we will just rewrite 10 to the seventh power underneath of our problem. Then we’re going to go ahead and add our coefficients, three point six plus two point one is five point seven and then we’ll do times 10 and then we’ll bring down the seven. So our solution will be five point seven times ten to the seventh power. All of these problems can be found on our adding and subtracting with scientific notation worksheet that can be downloaded from the link below.

Number three is a little trickier because it has one extra step we’re given seven point seven three times ten to the fifth minus five point three times ten to the fourth. Now in this case we cannot subtract these from each other because our exponents are not the same. You will notice this has a four and this has an exponent of five. They’re not equal which means we cannot subtract them we have to change one of them into the other and then once they are equal you can subtract them.

The easiest way to change the exponent on the power of 10 is to always make the smaller one into the larger one. What we’re going to do is we’re going to change this 4 into a 5. The way we do this is we move the decimal to the left one and we put it here and then we add one to our exponent. Every time you move the decimal to the left you will add one to the exponent. For example, let’s say we move the decimal instead of moving at once we move it one two times we would then add two to this exponent. It would be four plus two but if we did 4 plus 2 that would be 6 and we’re not trying to make 6 we’re trying to make five so adding two doesn’t make sense.  What we’re going to do is we’re going to move it left one time and then we’re going to add one because four plus one is five and we’re trying to make a five. We’re trying to make the exponents equal so let’s rewrite our problem.

Now we know that we have seven point seven three on this side times 10 to the fifth power minus, and now on this side we have point five 3 because we move the decimal left one time. 10 to the fifth power because it’s 4 plus 1 which would be 5. Now our exponents are equal, we have a 5 here and we have a 5 here so we can go ahead and subtract our coefficients. We’ll do seven point seven three minus 0.53 and then we’ll rewrite times 10. And then our power of 10 which is 10 to the fifth power because this is what we created to make them equal. Then we’ll go ahead and subtract our coefficients, seven point seven three minus 0.53 will be seven point two times 10 to the fifth power. And seven point two times 10 to the fifth power is going to be our solution. You can download our addition and subtraction with scientific notation worksheet by going to our website.