Adding and Subtracting in Scientific Notation Worksheet, Practice, and Video

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Key Points about Adding and Subtracting in Scientific Notation

Scientific Notation is a way of expressing very large or very small numbers in a more concise and manageable form.
To add or subtract numbers in Scientific Notation, the exponents must be the same.
Learning how to add and subtract in Scientific Notation is an important skill for anyone who works with numbers in scientific or engineering fields.

How to Add and Subtract in Scientific Notation

When Adding and Subtracting in Scientific Notation the exponents of the numbers you are adding or subtracting must be equal. If they are already equal, then you can just add the coefficients together. If the exponents are not equal, then you must make them equal by moving one of the decimals. The easiest way to make the decimals equal is to make the smaller exponent equal to the larger exponent by moving the decimal to the left. You add one to the exponent for each space that you move the decimal point to the left. Once the exponents are equal then you can add or subtract the coefficients. The final step for Adding and Subtracting in Scientific Notation is to ensure that the coefficient is between 1 and 10. If it is not, you must move the decimal point so that it is.

Scientific Notation is a way of expressing very large or very small numbers in a more concise and manageable form. It is widely used in scientific and engineering fields where accuracy and precision are of utmost importance. Adding and subtracting in Scientific Notation is a fundamental operation that is used frequently in various scientific calculations.

To add or subtract numbers in Scientific Notation, the exponents must be the same. If they are not, the numbers must be converted to the same exponent before proceeding with the operation. This may involve multiplying or dividing the numbers by powers of 10. Once the exponents are the same, the numbers can be added or subtracted just like regular numbers. The result must then be expressed in Scientific Notation again.

Learning how to add and subtract in Scientific Notation is an important skill for anyone who works with numbers in scientific or engineering fields. It allows for more accurate and efficient calculations, which can save time and reduce errors. By following some basic rules and examples, anyone can learn how to perform these operations with ease.

Common Core Standard: 8.EE.A.3
Related Topics: Square Roots, Cube Roots, Irrational Numbers, Powers of 10, Scientific Notation Intro, Converting Numbers to Scientific Notation, Converting Numbers from Scientific Notation, Multiplying in Scientific Notation, Dividing in Scientific Notation
Return To: Home, 8th Grade

What is Scientific Notation?

Scientific Notation is a method of writing numbers as a product of a base number and a power of 10. It is also known as standard form or exponential notation. This notation is particularly useful when dealing with very large or very small numbers, as it makes them easier to read and work with.

In Scientific Notation, a number is written in the form a × 10n, where a is a number between 1 and 10, and n is an integer. The number a is called the base, and n is called the exponent or power of 10. The exponent n indicates how many times the base must be multiplied by 10 to get the original number.

For example, the number 3,000,000 can be written in Scientific Notation as 3 × 106. Here, the base is 3, and the exponent is 6, indicating that 3 must be multiplied by 10 six times to get the original number.

On the other hand, the number 0.00000005 can be written in Scientific Notation as 5 × 10-8. Here, the base is 5, and the exponent is -8, indicating that 5 must be divided by 10 eight times to get the original number.

Scientific Notation is widely used in science, engineering, and mathematics to express very large or very small numbers in a concise and standardized way.

Adding in Scientific Notation

Adding in Scientific Notation is a fundamental operation in math that is used to simplify calculations involving large and small numbers. It involves adding numbers that are expressed in scientific notation, which is a way of writing numbers as a product of a decimal number and a power of ten.

To add numbers in scientific notation, the first step is to make sure that the exponents are the same. If the exponents are not the same, then one of the numbers must be converted so that the exponents are equal. This is done by moving the decimal point to the right or left and adjusting the exponent accordingly.

Once the exponents are the same, the decimal numbers can be added or subtracted, and the result can be expressed in scientific notation. To do this, the decimal point is moved so that there is only one non-zero digit to the left of the decimal point, and the exponent is adjusted accordingly.

For example, to add 3.4 x 10^4 and 2.1 x 10^3, the first step is to convert 2.1 x 10^3 to 0.21 x 10^4 by moving the decimal point one place to the left. Then, the two numbers can be added to get 3.61 x 10^4.

It is important to note that when adding or subtracting numbers in scientific notation, the final result should always be expressed in scientific notation. This means that the decimal point should be moved so that there is only one non-zero digit to the left of the decimal point, and the exponent should be adjusted accordingly.

Calculators can be used to simplify the process of adding numbers in scientific notation. Many scientific calculators have a function that allows users to enter numbers in scientific notation and perform calculations. There are also online calculators that can be used to add numbers in scientific notation.

In summary, adding in scientific notation involves making sure that the exponents are the same, adding or subtracting the decimal numbers, and expressing the result in scientific notation. Calculators can be used to simplify the process, but it is important to understand the underlying math concepts to ensure accurate calculations.

Subtracting in Scientific Notation

Subtracting in scientific notation is similar to adding in scientific notation. The only difference is that you need to subtract the coefficients instead of adding them. To subtract two numbers in scientific notation, you must make sure that the exponents are the same. If the exponents are not the same, then you need to adjust one or both of the numbers so that they have the same exponent.

Here is an example of subtracting in scientific notation:

(4.1 * 10^-2) – (2.6 * 10^-3)

First, adjust the second number so that it has the same exponent as the first number. In this case, you need to multiply 2.6 * 10^-3 by 10^1 to get:

(4.1 * 10^-2) – (2.6 * 10^-3 * 10^1)

Simplify the second number by multiplying the coefficient and the exponent:

(4.1 * 10^-2) – (26 * 10^-3)

Now you can subtract the coefficients:

(4.1 – 26) * 10^-3

Simplify the subtraction:

-21.9 * 10^-3

Finally, express the answer in scientific notation:

-2.19 * 10^-2

You can use a calculator to subtract numbers in scientific notation. Simply enter the numbers into the calculator and follow the instructions to subtract them. However, it’s important to understand the steps involved in subtracting in scientific notation so that you can check your work and understand the calculations.

How to Add and Subtract Scientific Notation with Different Exponents

When adding or subtracting numbers in scientific notation with different exponents, the first step is to rewrite the numbers so that they have the same exponent. This can be done using the distributive property of exponents.

Example:

Add 3.2 x 10^4 and 2.5 x 10^6

Step 1: Rewrite the numbers so that they have the same exponent.

3.2 x 10^4 = 0.32 x 10^5

2.5 x 10^6 = 25 x 10^4

Step 2: Now that the exponents are the same, add the coefficients.

0.32 x 10^5 + 25 x 10^4 = 0.32 x 10^5 + 2.5 x 10^5

Step 3: Rewrite the answer in scientific notation.

0.32 x 10^5 + 2.5 x 10^5 = 2.82 x 10^5

Explanation:

In the example above, the distributive property of exponents was used to rewrite the numbers so that they had the same exponent. This was done by multiplying and dividing by powers of 10. Once the exponents were the same, the coefficients were added as usual.

When subtracting numbers in scientific notation with different exponents, the same process is followed. The numbers are rewritten so that they have the same exponent, and then the coefficients are subtracted.

Example:

Subtract 7.6 x 10^3 from 2.4 x 10^5

Step 1: Rewrite the numbers so that they have the same exponent.

7.6 x 10^3 = 0.076 x 10^5

2.4 x 10^5 = 24 x 10^3

Step 2: Now that the exponents are the same, subtract the coefficients.

24 x 10^3 – 0.076 x 10^5 = 24 x 10^3 – 7.6 x 10^3

Step 3: Rewrite the answer in scientific notation.

24 x 10^3 – 7.6 x 10^3 = 1.66 x 10^4

3 Simple Adding Scientific Notation Examples

Adding numbers in scientific notation involves adding the coefficients of the numbers and keeping the base and exponent the same.

Check to see if the exponents on the power of tens are equal.
If the exponents are equal, then you can add or subtract the coefficients.
If the exponents are not equal, you must make them equal by moving the decimal point.
Moving a decimal point to the left will add to the exponent for each digit that it moves left.
Once the exponents are equal, you can add or subtract the coefficients.
Make sure that your coefficient is in between one and ten since it must be written in Scientific Notation.

Here are some examples of adding numbers in scientific notation:

Example 1

Add 3.2 x 10^5 and 2.5 x 10^4.

To add these numbers, you need to make sure that they have the same exponent. In this case, you can rewrite 2.5 x 10^4 as 0.25 x 10^5. Then, you can add the coefficients:

3.2 x 10^5 + 0.25 x 10^5 = 3.45 x 10^5

Therefore, the sum of 3.2 x 10^5 and 2.5 x 10^4 is 3.45 x 10^5.

Example 2

Add 6.7 x 10^3 and 4.2 x 10^2.

To add these numbers, you need to rewrite 4.2 x 10^2 as 0.42 x 10^3. Then, you can add the coefficients:

6.7 x 10^3 + 0.42 x 10^3 = 7.12 x 10^3

Therefore, the sum of 6.7 x 10^3 and 4.2 x 10^2 is 7.12 x 10^3.

Example 3

Add 5.6 x 10^4 and 3.9 x 10^3.

To add these numbers, you need to rewrite 3.9 x 10^3 as 0.39 x 10^4. Then, you can add the coefficients:

5.6 x 10^4 + 0.39 x 10^4 = 5.99 x 10^4

Therefore, the sum of 5.6 x 10^4 and 3.9 x 10^3 is 5.99 x 10^4.

3 Easy Subtracting Scientific Notation Examples

Subtracting numbers in scientific notation can be done by following a few simple steps. First, make sure that the bases of the two numbers are the same. Then, subtract the coefficients and keep the base and exponent the same.

For example, let’s subtract 3.2 x 10^5 from 6.8 x 10^5. Since the bases are the same, we can subtract the coefficients and keep the base and exponent the same. Therefore, the answer is 3.6 x 10^5.

Here are a few more examples of subtracting numbers in scientific notation:

(4.5 x 10^4) – (2.3 x 10^4) = 2.2 x 10^4
(8.2 x 10^6) – (6.1 x 10^6) = 2.1 x 10^6
(3.7 x 10^3) – (2.4 x 10^3) = 1.3 x 10^3

It is important to note that when subtracting numbers in scientific notation, the exponent of the resulting number should always be the same as the exponents of the numbers being subtracted.

5 Quick Adding and Subtracting Scientific Notation Practice Problems

Adding and Subtracting Scientific Notation Rules

When adding or subtracting numbers in scientific notation, the powers of ten must be the same. If the powers of ten are not the same, then one of the numbers must be converted to match the other. This can be done by increasing or decreasing the power of ten while adjusting the coefficient accordingly.

To add or subtract numbers in scientific notation, follow these rules:

Adjust the powers of ten in the two numbers so that they are the same.
Add or subtract the coefficients of the two numbers.
Write the answer in scientific notation.

Here are some examples to illustrate these rules:

Example 1: Add 2.6 x 10^4 and 3.8 x 10^3.

Step 1: Adjust the powers of ten so they are the same. Since 3.8 x 10^3 has a smaller power of ten, it needs to be converted to match 2.6 x 10^4. Multiply 3.8 by 10 to get 38, and decrease the power of ten by 1 to get 10^3.

2.6 x 10^4 + 38 x 10^3 = 2.6 x 10^4 + 3.8 x 10^4

Step 2: Add the coefficients.

2.6 + 3.8 = 6.4

Step 3: Write the answer in scientific notation.

6.4 x 10^4

Example 2: Subtract 5.6 x 10^7 from 8.2 x 10^7.

Step 1: Adjust the powers of ten so they are the same. Since 5.6 x 10^7 has a smaller power of ten, it needs to be converted to match 8.2 x 10^7. Multiply 5.6 by 10 to get 56, and increase the power of ten by 1 to get 10^8.

8.2 x 10^7 - 56 x 10^6 = 8.2 x 10^7 - 5.6 x 10^7

Step 2: Subtract the coefficients.

8.2 - 5.6 = 2.6

Step 3: Write the answer in scientific notation.

2.6 x 10^7

It is important to note that the distributive property can also be used when adding or subtracting numbers in scientific notation. This property states that a number outside of a set of parentheses can be distributed to each term inside the parentheses.

For example, to add (3.2 x 10^6) + (2.4 x 10^6), the distributive property can be used as follows:

(3.2 + 2.4) x 10^6 = 5.6 x 10^6

In summary, adding and subtracting in scientific notation requires adjusting the powers of ten and then adding or subtracting the coefficients. The distributive property can also be used to simplify the process.

How to Add in Scientific Notation

To add numbers in scientific notation, the powers of 10 must be the same for both numbers. Here are the steps to follow:

Adjust the powers of 10 in the two numbers so that they have the same exponent. It is easier to adjust the smaller exponent to equal the larger exponent.
Add the coefficients of the two numbers.
If necessary, adjust the sum so that it is in scientific notation.

For example, to add 3.2 x 10^5 and 7.5 x 10^4, follow these steps:

Adjust the powers of 10: 7.5 x 10^4 becomes 0.75 x 10^5.
Add the coefficients: 3.2 + 0.75 = 3.95.
Adjust the sum: 3.95 x 10^5 is already in scientific notation.

Another example: to add 2.1 x 10^3 and 4.5 x 10^2, follow these steps:

Adjust the powers of 10: 4.5 x 10^2 becomes 0.45 x 10^3.
Add the coefficients: 2.1 + 0.45 = 2.55.
Adjust the sum: 2.55 x 10^3 is already in scientific notation.

It is important to note that when adding or subtracting numbers in scientific notation, the result should also be in scientific notation. This means that the coefficient should be between 1 and 10 and the exponent should be a multiple of 3.

It is also important to be careful when adding numbers with opposite signs. If the coefficients are close in value, the result may have fewer significant figures than the original numbers. In this case, it may be necessary to round the result to the appropriate number of significant figures.

How to Subtract Scientific Notation

Subtracting numbers in scientific notation is similar to adding them. The first step is to adjust the powers of 10 so that they have the same exponent. Once the exponents are the same, the coefficients can be subtracted or added. Finally, the answer is expressed in scientific notation.

Here are the steps to subtract numbers in scientific notation:

Adjust the powers of 10: Adjust the powers of 10 in the two numbers so that they have the same exponent. This is done by moving the decimal point to the left or right and adjusting the exponent accordingly. It is easier to adjust the smaller exponent to equal the larger one.
Subtract the coefficients: Once the exponents are the same, subtract the coefficients. If the coefficients have different signs, add their absolute values and use the sign of the larger coefficient. If the coefficients have the same sign, subtract their absolute values and use the sign of the larger coefficient.
Express the answer in scientific notation: Finally, express the answer in scientific notation by writing the coefficient as a number between 1 and 10 and multiplying it by 10 raised to the exponent.

Here is an example:

Subtract 4.5 x 10^5 from 8.2 x 10^6.

Adjust the powers of 10: Since 5 is smaller than 6, adjust the first number by multiplying it by 10. So, 4.5 x 10^5 becomes 4.5 x 10^6.
Subtract the coefficients: Now that the exponents are the same, subtract the coefficients. 8.2 – 4.5 = 3.7.
Express the answer in scientific notation: Finally, express the answer in scientific notation by writing 3.7 as 3.7 x 10^6.

Therefore, the difference between 8.2 x 10^6 and 4.5 x 10^5 is 3.7 x 10^6.

Remember, practice makes perfect, so keep practicing subtracting numbers in scientific notation until you feel confident with the process.

Adding and Subtracting Scientific Notation FAQ

How do you add scientific notation with different exponents?

When adding or subtracting scientific notation with different exponents, the exponents must be the same. To do this, you need to convert one or both numbers so that they have the same exponent. This can be done by multiplying or dividing by a power of ten. Once the exponents are the same, you can add or subtract the numbers as usual.

What are the rules for adding and subtracting, multiplying and dividing scientific notations?

The rules for adding and subtracting, multiplying and dividing scientific notation are as follows:

When adding or subtracting, the exponents must be the same.
When multiplying, you add the exponents.
When dividing, you subtract the exponents.

What is the rule for adding in scientific notation?

The rule for adding in scientific notation is to add the coefficients and keep the exponent the same.

What must you be sure of when adding and subtracting using scientific notation?

When adding and subtracting using scientific notation, you must be sure that the exponents are the same. If they are not the same, you need to convert one or both numbers so that they have the same exponent.

How do you subtract scientific notation using a calculator?

To subtract scientific notation using a calculator, you can use the subtraction key just like you would for regular numbers. However, you need to make sure that the exponents are the same before you subtract the coefficients.

What are some notes to keep in mind when adding and subtracting scientific notation?

When adding and subtracting scientific notation, it is important to keep the following notes in mind:

Make sure the exponents are the same before adding or subtracting.
Be careful when adding or subtracting negative numbers.
Watch out for rounding errors when using a calculator.

Adding and Subtracting Scientific Notation Worksheet Video Explanation

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.