How to Divide Scientific Notation: Everything you Need to Know

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A Brief Description of Dividing in Scientific Notation

When Dividing in Scientific Notation you divide the coefficients that are in the problem. Dividing in Scientific Notation is different then Adding or Subtracting because you do not have to make the exponents equal beforehand. When dividing the coefficients, you will subtract the exponents. After you divide, check your answer to make sure the coefficient is in between 1 and 10. If the coefficient is not in between 1 and 10, you must move the decimal to make it in between 1 and 10. You add to the exponent for each space that you moved the decimal to the left. You subtract from the exponent for each space that you moved the decimal to the right.

Common Core Standard: 8.EE.A.3

Return To: Home, 8th Grade

Here’s how to answer any Dividing in Scientific Notation Example Problem

So how to divide numbers in scientific notation easily? When Dividing in Scientific Notation you divide the coefficients of the number written in Scientific Notation. When learning how to divide Scientific Notation you will follow the same rules as when dividing exponential terms. That is to say that when you divide the Powers of Ten together you must subtract the exponents. After you divide, check your solution to ensure the coefficient is in the middle of 1 and 10. In the event that the coefficient isn’t in the middle of 1 and 10, you should move the decimal to make it in the middle of 1 and 10. You add to the power for each digit that you move the decimal left. You subtract from the power for each space that you moved the decimal right.

5 Short Steps for Dividing in Scientific Notation

Divide the coefficients together.
Subtract the exponents of the power of ten from each other.
If the coefficient is in between 1 and 10 then you are done solving.
If the coefficient is not in between 1 and 10, then you must move the decimal either left or right to make the coefficient in between 1 and 10.
If you move the decimal left, you add to the exponent, if you move the decimal right, you subtract from the exponent.

Dividing in Scientific Notation Practice Problems Quiz

Watch the how to Divide in Scientific Notation Video Explanation

Watch our free video on how to solve Dividing in Scientific Notation. This video shows how to solve problems that are on our free Divide Scientific Notation worksheet that you can get by submitting your email above.

Watch the free Divide Scientific Notation video on YouTube here: How to Divide Scientific Notation

Video Transcript:

This video is about how to dividing scientific notation. You can get the dividing scientific notation worksheet we use in this video for free by clicking on the link in the description below.

In order to show you how to divide scientific notation, we’re going to do a couple problems from our scientific notation division worksheet. When dividing in scientific notation you will take the coefficients of the numbers written in scientific notation and you will divide them. Then you will take the powers of 10 and you will subtract the exponents. If you can think about when you divide exponents we know that when we divide exponents you subtract them so if you were just given the problem 10 to the seventh divided by 10 to the fifth, you would do 10 to the seventh minus 5. You would subtract the exponents and you would get 10 squared. This rule for exponents still applies to our numbers in scientific notation here. Even though they’re in scientific notation division, the rules for the exponent will still remain the same so you will still subtract these.

The first problem we are going to practice to show dividing with scientific notation is number 2. Number 2 gives us 4 point 2 times 10 to the seventh divided by 2 point one times 10 to the fifth. We’re going to take the coefficients which are 4 point 2 and 2 point 1 and we will divide them. We have four point two divided by two point one that is going to be multiplied times our power of 10, which in this case is 10 to the seventh divided by 10 to the fifth. We already know that when we divide exponents we subtract them so we’re going to do 10 to the 7 minus 5. Four point two divided by two point one is two and then our power of 10 will be 10 to the 7 minus 5 which is also 2. Our solution to this problem will be 2 times 10 to the 2nd power. This is how to divide with scientific notation in an easy way.

The next problem is number 3. This problem is about how to divide scientific notation with different exponents. It gives us 4 times 10 to the 9th divided by 2 times 10 to the fourth. Once again when you divide in scientific notation you’re going to take your coefficients and your to divide them. We’re gonna do four divided by two times our power of 10 which will be ten to the ninth minus ten to the fourth, or just nine minus four because we’re dividing. We’re subtracting the exponents four divided by two is two and then 10 to the ninth minus four is nine minus 4 which is five. So our solution is two times ten to the fifth power. This is the easiest way to learn dividing numbers in scientific notation.

The last problem we’re going to do to show you how to divide with scientific notation is number six. This problem gives us nine point three times ten to the seventh divided by three times ten to the thirteenth. Once again we’ll take our coefficients which are nine point three and three and we will divide them. Nine point three divided by three we’re going to write times our power of ten, which in this case we’re gonna do 10 to the seventh minus 10 to the 13th or just seven minus 13. When we divide nine point three divided by three it’s three point one times ten and then seven minus 13 is negative six. Our solution to this will be three point one times 10 to the negative sixth power. This has been three examples of division of scientific notation practice problems. You can try all the practice problems by downloading the free dividing numbers in scientific notation worksheet above.