How to Multiply Scientific Notation in 5 Easy Steps

A Short Guide for Multiplying in Scientific Notation

Here’s how to complete any Multiplying in Scientific Notation Example Problem

So how to multiply with scientific notation anyway? When Multiplying in Scientific Notation you multiply the coefficients of the number written in Scientific Notation. When learning how to multiply Scientific Notation you will follow the same rules as when multiplying exponential terms. That is to say that when you multiply the Powers of Ten together you must add the exponents. After you multiply, 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.

1. Multiply the coefficients together.
2. Add the exponents of the power of ten together.
3. If the coefficient is in between 1 and 10 then you are done solving.
4. 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.
5. If you move the decimal left, you add to the exponent, if you move the decimal right, you subtract from the exponent.

 

Multiplying Scientific Notation Practice Problems Quiz

Watch the How to Multiply in Scientific Notation Video Explanation

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

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

Video Transcript:

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

Here we are at our first problem for scientific notation multiplication and we have to multiply our two numbers written in scientific notation together. When multiplying numbers in scientific notation you are going to multiply the two coefficients together. In this case our coefficients are nine and two. We will multiply these together and then you will add the exponents of three and five, just like if you were to follow the rule for multiplying exponents. If we wanted to multiply 10 to the third times 10 to the fifth, we would keep the base of 10 and then we would add three plus five, which would equal 10 to the 8th. You will follow the same rule when multiplying numbers in scientific notation and finding out how do you multiply scientific notation. Let’s go ahead and solve our first problem.

9 times 10 to the 3rd times 2 times 10 to the 5th. Like we already said we have to multiply the coefficients together. We’re going to do 9 times 2 because we’re multiplying and that’s gonna be times and then we have our 2 powers of 10 which are 10 to the third and 10 to the fifth. That will be times 10 to the 3 plus 5 because we have to add the exponents 9 times 2 is 18 times 10 to the 3 plus 5 which is 8. Now 18 times 10 to the 8th is the result of multiplying these together, however, 18 is not in scientific notation. This coefficient here has to be in between 1 and 10.

What we’re going to do is we’re going to take our decimal we’re gonna move it to the left once. And then we’re going to add 1 to the exponent. Every time you move the decimal to the left you will add to the exponent. For example, if we had to move the decimal 2 times we would add two to the exponent but in this case we only have to move the decimal one time to make a number in between one and ten. We only add one to the exponent, so after we move the decimal one time it becomes 1.8 times 10 to the 8 plus 1, which is ninth power. Our final solution is 1.8 times 10 to the ninth power.

Number 4 on the multiplying with scientific notation worksheet gives us 4 point 2 times 10 to the first times 6 point 5 times 10 to the ninth. This problem shows how to multiply scientific notation with different exponents. We already know that when we multiply in scientific notation, we’re going to take our coefficients and we’re going to multiply them together. So we’re going to do four point two times six point five times our power of 10, which is 10 to the 1st plus 9 because this one’s 10 to the ninth. We will do four point two times six point five which is twenty seven point three times 10 to the 1 plus nine which is 10. Now once again our coefficient here has to be in between 1 and 10 so we have to take our decimal and moved it left once so that it becomes two point seven three which is in between 1 and 10. And then add one to the exponent because we move the decimal to the left so  this will become two point seven three times 10 to the 10 plus one power, which is to the 11th and this is going to be our final solution. This is how to multiply numbers in scientific notation.

The last problem we’re going to do to show you how to multiply numbers written in scientific notation is number five. This problem gives us 3 times 10 to the 15th times 8 times 10 to the 12th. Once again we will multiply our coefficients together. We’ll do 3 times 8 times our power of 10, which in this case is 10 to the 15th and 10 to the 12th. 10 to the 15 plus 12 3 times 8 is 24 times 10. And then our power is going to be 15 plus 12 which is 27. Then our coefficient here is 24 that is not in between ten so we have to move the decimal from 24 to 2.4. That it’s in between 1 and 10 and then because we move the decimal left once we will add 1 to our exponent so this will become 2 point 4 times 10 to the 28th power, which is our answer. You can try all the practice problems by downloading the free multiplying with scientific notation worksheet above.