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How to Add and Subtract in Scientific Notations? (+FREE Worksheet!)

Scientific notation is one of the most common methods in mathematics for displaying very large and very small numbers that make calculations with those numbers easier. This article teaches you how to add and subtract in Scientific Notations using a few simple steps.

Scientific notation is one of the most common methods in mathematics for displaying very large and very small numbers that make calculations with those numbers easier. With a scientific notation, each number can be written as a product of two numbers.

To add or subtract numbers in scientific notion, we need to have the same power of the base (number \(10\)), and only decimal parts are added or subtracted.

Related Topics

• How to Round Decimals
• How to Multiply and Divide Decimals
• How to Add and Subtract Decimals
• How to Compare Decimals

Step by step guide to Add and Subtract Scientific Notations

Adding and subtracting numbers in scientific notion:

• Step 1: Adjust the powers in the numbers so that they have the same power. (It is easier to adjust the smaller power to equal the larger one)
• Step 2: Add or subtract the numbers (only decimal parts).
• Step 3: Convert the answer to scientific notation if needed.

Addition and Subtraction in Scientific Notation– Example 1:

Write the answer in scientific notation. \(11\times 10^7 -\ 4.4\times 10^7=\)

Since two numbers have the same power, factor \(10^7\) out: \( (11 -\ 4.4 ) \times 10^7 = 6.6\times 10^7\)

Addition and Subtraction in Scientific Notation– Example 2:

Write the answer in scientific notation. \(9.7\times 10^4 -\ 33\times 10^3=\)

Convert the second number to have the same power of \(10 \): \(33\times 10^3=3.3\times 10^4\).

Now, two numbers have the same power of \(10 \). Subtract: \( 9.7\times 10^4 -\ 3.3\times 10^4 = (9.7 -\ 3.3 ) \times 10^4 = 6.4\times 10^4\)

Addition and Subtraction in Scientific Notation– Example 3:

Write the answer in scientific notation. \(3.5\times 10^6 +\ 4.7\times 10^6=\)

Since two numbers have the same power, factor \(10^6\) out: \( (3.5 +\ 4.7 ) \times 10^6 = 8.2\times 10^6\)

Addition and Subtraction in Scientific Notation– Example 4:

Write the answer in scientific notation. \(2.6\times 10^8 +\ 4.4\times 10^7=\)

Convert the second number to have the same power of \(10 \): \(4.4\times 10^7=0.44\times 10^8\).

Now, two numbers have the same power of \(10 \). Add: \( 2.6\times 10^8 +\ 0.44\times 10^8 = (2.6 +\ 0.44 ) \times 10^8 = 3.04\times 10^8\)

Exercises for Adding and Subtracting Scientific Notations

Write the answer in scientific notation..

• \(\color{blue}{5.1\times 10^5 +\ 3.9\times 10^5=}\)
• \(\color{blue}{8.9\times 10^7 -\ 6.9\times 10^7=}\)
• \(\color{blue}{1.2\times 10^4 +\ 3\times 10^3=}\)
• \(\color{blue}{5.3\times 10^6 -\ 2.2\times 10^5=}\)
• \(\color{blue}{1.6\times 10^9 +\ 4.8\times 10^9=}\)
• \(\color{blue}{9.8\times 10^3 -\ 6.1\times 10^3=}\)
• \(\color{blue}{9\times 10^5}\)
• \(\color{blue}{2\times 10^7}\)
• \(\color{blue}{1.5\times 10^4}\)
• \(\color{blue}{5.08\times 10^6}\)
• \(\color{blue}{6.4\times 10^9}\)
• \(\color{blue}{3.7\times 10^3}\)

by: Effortless Math Team about 3 years ago (category: Articles , Free Math Worksheets )

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Scientific Notation Addition and Subtraction

How to Add and Subtract Values in Scientific Notation - Addition and subtraction are one of the basic topics taught to children. However, when we move towards learning harder concepts, operation on values in scientific notations comes into the picture. Let us learn sequentially with the help of examples. 4.5× 10 4 + 1.7× 10 5 . Firstly, we need to ensure that both exponents have the same value. Thus, we need to change the value of 1.7 x 105 to 17 x 104. If both already had the same exponential value, you can neglect this step. 4.5× 10 4 + 17 × 10 4 . Now, we will take exponentials common and add the decimal values. (4.5+ 17) × 10 4 | 21.5 × 10 4 . Similar steps are taken for the subtraction phase we just need to retrace our steps and find differences rather than sums. These lessons and worksheets show you how to perform sums and differences with values that are in scientific notation.

Aligned Standard: 8.EE.A.4

• Products of Sci. Notation Step-by-Step Lesson - Help the dinosaur jam through this one!
• Guided Lesson - I spent a little more time working on differences here.
• Guided Lesson Explanation - Sometimes it is easier to transfer to standard form first.
• Practice Worksheet - Five products and five differences for you to wrap your head around.
• Matching Worksheet - These matches can actually be determined by the front numbers. Don't get tricked by the powers of ten used.
• Answer Keys - These are for all the unlocked materials above.

Homework Sheets

Get in the habit of writing a parenthesis to help you solve it.

• Homework 1 - The first thing that you want to do is to get all of the powers of ten to the same exponent.
• Homework 2 - Since these are all powers of ten you can easily slide up and down by just moving the decimal point.
• Homework 3 - You can also convert the numbers to standard form when it suits you. You would need to convert it back.

Practice Worksheets

In my travels, I have found that students have more problem with the differences.

• Practice 1 - Since these are all powers of ten you can easily slide up and down by just moving the decimal point.
• Practice 2 - It all start on the front end and then transitions to the back end.
• Practice 3 - Work on both ends of the problem.

Math Skill Quizzes

Three to four sum problems followed by six to seven difference problems.

• Quiz 1 - Find the difference of: 7 x 10 4 - 1.7 x 10 2
• Quiz 2 - Find the difference of: 16 x 10 2 - 44 x 10 4
• Quiz 3 - You would need to convert it back.

When Will You Need to Perform Basic Math Operations with Scientific Notation?

The basic benefit by using scientific forms of values is to be able to quickly communicate humongous or microscopic numbers. Using this form of number notation really makes it easy to write accurate values. There is also another added benefit. When you wish to perform addition or subtraction, it helps make it much faster. This form of notation is sometimes referred to as floating-point because it is based on the base ten system where everything differs by a power of ten. The exponential value expresses the position of decimal point and how many zeros with appear before or after the whole decimal value. Keeping track of that exponential value can prove to be a bit tricky, but if you organize yourself well, it is not bad at all. The more you space out your problems and rewrite them, the easier it will be for you. Take a look at this problem: (2.5 x 10 3 ) + (4.25 x 10 5 ). Right away you notice that the powers of ten differ and will run into difficult. You can restate the problem using the exponent property. The exponent property tells us that b m x b n = b (m + n) Using this well-known property, we can start the problem by rewriting it as: (2.5 x 10 3 ) + (4.25 x 10 2 x 10 3 ) Since we have now established a common exponent, we can work the problem further. It would also help us to organize it with a bracket. We can write this as: (2.5 x 10 3 ) + [(4.25 x 10 2 ) x 10 3 ] (2.5 x 10 3 ) + (425 x 10 3 ) Now that we have everything in the same format, we can just continue on with solving our operations. (2.5 + 425) x 10 3 (427.5) x 10 3 We can then restate this value in proper scientific notation: (427.5) x 10 3 = (4.275 x 10 2 ) x 10 3 4.275 x 10 5 We demonstrated the addition operation, but subtraction is done in much the same way. Like we said before, it is of the utmost importance that you continual space things out and write as much as possible. Restate the problem every step along the way and it will be easy to track.

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Add & Subtract Scientific Notation Worksheets

Related Topics: More Math Worksheets More Grade 7 Math Lessons Grade 7 Math Worksheets

There are five sets of scientific notation worksheets:

• Scientific to Standard Notation
• Standard to Scientific Notation
• Multiply Scientific Numbers
• Divide Scientific Numbers
• Add & Subtract Scientific Numbers

Examples, solutions, videos, and worksheets to help Grade 7 and Grade 8 students learn how to add & subtract numbers in scientific notation.

How to add & subtract numbers in scientific notation?

There are two sets of dividing numbers in scientific notation worksheets.

• Add & Subtract numbers in scientific notation (positive exponents).
• Add & Subtract numbers in scientific notation (include negative exponents)

These are the steps to add & subtract numbers in scientific notation:

• Make sure that the exponents of both numbers are the same. If they are not the same, adjust one or both of the numbers so that they have the same exponent.
• Add or subtract the coefficients of the numbers.
• Keep the common exponent from step 1.
• Adjust the result to scientific notation if needed.

Example: (3.52 x 10 5 ) + (2.6 x 10 2 )

• Since the numbers have different exponents, we need to adjust them before adding.
• Adjust the second number to have an exponent of 5: 2.6 x 10 2 = 0.0026 x 10 5
• Add the coefficients: 3.52 + 0.0026 = 3.5226
• Keep the common exponent 10 5 .
• The result is 3.5226 x 10 5 .

Example: (4.33 x 10 3 ) − (3.6 x 10 4 )

• Since the numbers have different exponents, we need to adjust them before subtracting.
• Adjust the second number to have an exponent of 3: 3.6 x 10 4 = 36 x 10 3
• Subtract the coefficients: 4.33 - 36 = -31.67
• Keep the common exponent 10 3 .
• Adjust the result is -31.67 x 10 3 = -3.167 x 10 4

Click on the following worksheet to get a printable pdf document. Scroll down the page for more Add & Subtract Scientific Notation Worksheets .

More Add & Subtract Scientific Notation Worksheets

Printable (Answers on the second page.) Scientific Notation Worksheet #1 (positive exponents) Scientific Notation Worksheet #2 (include negative exponents)

Related Lessons & Worksheets

Add & Subtract Numbers in Scientific Notation

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Addition and Subtraction with Scientific Notation Worksheets

• Pre-Algebra >
• Scientific Notation >
• Addition and Subtraction

Whiz past our free, printable addition and subtraction with scientific notation worksheets, which encapsulate arithmetic operations on big and small numbers. Apply the rules of addition and subtraction, while deftly handling exponential forms. Simplicity is key, so break down complex expressions before you start calculating.

Our pdf worksheets on adding and subtracting numbers in scientific notation are ideal for students in grade 8.

Add and Subtract Numbers with Positive Powers in Scientific Notation

A perfect place to start, these addition and subtraction with scientific notation worksheet pdfs center around positive powers of ten to keep children on their toes.

Adding and Subtracting Numbers in Scientific Notation

Diversity is the hallmark of these printable worksheets on addition and subtraction with scientific notation, where children practice both negative and positive powers.

Adding and Subtracting Decimals in Scientific Notation

An exciting challenge for math enthusiasts in 8th grade, these pdf worksheets on adding and subtracting numbers in scientific notation are buoyed by decimals.

Operations with Scientific Notation Worksheets | Mixed Review

Finish with a flourish through these printable mixed exercises featuring all four operations with scientific notation, designed to please math lovers in grade 8.

Related Printable Worksheets

▶ Multiplication and Division with Scientific Notation

▶ Scientific Notation of Large Numbers

▶ Scientific Notation of Small Numbers

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Table of Contents

Last modified on August 3rd, 2023

#ezw_tco-2 .ez-toc-title{ font-size: 120%; ; ; } #ezw_tco-2 .ez-toc-widget-container ul.ez-toc-list li.active{ background-color: #ededed; } chapter outline

Adding and subtracting numbers in scientific notation.

Adding or subtracting numbers in scientific notation requires the numbers to have similar bases and exponents. This is necessary to ensure that the corresponding integers in their coefficients have the same place value.

Adding in Scientific Notation with Examples

A few steps we should follow while adding numbers in scientific notation are:

• Check if the exponents of the numbers are equal or not.
• If they are equal, factor out the numbers using the distributive property of multiplication (a m  x a n  = a m + n ). 
• Add the coefficients. If unequal, the exponents should be made equal by moving the decimal point. The easiest way to make the decimals equal is to make the smaller exponent equal to the larger exponent by shifting the decimal to the left.

Let us understand the concept with a few examples.

With Equal Exponents

Example – 1

Add: (4.7 x 10 3 ) + (1.89 x 10 3 )

• These two numbers have similar exponents
• Using the distributive property of multiplication; the numbers are factored out as shown below:

(4.7 x 10 3 ) + (1.89 x 10 3 )

(4.7 + 1.89) × 10 3

• Adding the coefficients and multiplying by the power of 10, we get = 6.59 × 10 3

Thus, the answer is 6.59 × 10 3

With Unequal Exponents

Example – 2

Add:  (8.8 x 10 3 ) + (6.25 x 10 5 )

Here, the powers of the numbers are different. Thus we need to manipulate the power with a larger exponent.

Using the property of exponents:  a m  x a n  = a m + n , rewriting the larger exponent 10 5 into (10 2 × 10 3 )

= (8.8 x 10 3 ) + (6.25 x 10 5 )

= (8.8 x 10 3 ) + (6.25 x 10 2 × 10 3 )

= (8.8 x 10 3 ) + [(6.25 x 10 2 ) × 10 3 ]

= (8.8 x 10 3 ) + (625 × 10 3 )

= (8.8 + 625) × 10 3

Adding the coefficients and multiplying by the power of 10, we get

 = 633.8 × 10 3

Thus, the answer is 633.8 × 10 3

(3.769 x 10 5 ) + (4.21 x 10 5 )

These two numbers have similar exponents Using the distributive property of multiplication; the numbers are factored out as shown below: (3.769 x 10 5 ) + (4.21 x 10 5 ) (3.769 + 4.21) × 10 5 Adding the coefficients and multiplying by the power of 10, we get = 7.979 × 10 5 Thus, the answer is 7.979 × 10 5

Add:  (5.5 x 10 2 ) + (1.25 x 10 4 )

Here, the powers of the numbers are different. Thus we need to manipulate the power with a larger exponent. Using the property of exponents:  a m  x a n  = a m + n , rewriting the larger exponent 10 5 into (10 2 × 10 3 ) = (5.5 x 10 2 ) + (1.25 x 10 4 ) = (5.5 x 10 2 ) + (6.25 x 10 2 × 10 3 ) = (8.8 x 10 3 ) + [(6.25 x 10 2 ) × 10 3 ] = (8.8 x 10 3 ) + (625 × 10 3 ) = (8.8 + 625) × 10 3 Adding the coefficients and multiplying by the power of 10 we get  = 633.8 × 10 3 Thus, the answer is 633.8 × 10 3

Subtracting in Scientific Notation with Examples

The basic steps to subtract two or more numbers in scientific notation are the same as that of addition, except that addition is replaced by subtraction.

Let us consider a few examples.

Subtract: (4 x 10 -2 ) – (2.89 x 10 -2 )

= (4.4 x 10 2 ) – (2.89 x 10 2 )

= (4.4 – 2.89) × 10 2

• Adding the coefficients and multiplying by the power of 10, we get = 1.51 × 10 2

Thus, the answer is 1.51 × 10 2

Subtract:  (7.35 x 10 7 ) – (5.8 x 10 4 )

Using the property of exponents:  a m  x a n  = a m + n , rewriting the larger exponent 10 7 into (10 3 × 10 4 )

= (7.35 x 10 7 ) – (5.8 x 10 4 )

= (7.35 x 10 3 × 10 4 ) – (5.8 x 10 4 )

= [(7.35 x 10 3 ) × 10 4 ] – (5.8 x 10 4 )

= (7350 × 10 4 ) – (5.8 x 10 4 )

= (7350 – 5.8) × 10 4

Adding the coefficients and multiplying by the power of 10, we get = 7,344.2 × 10 4

Thus, the answer is 7,344.2 × 10 4

Subtract: (6 x 10 5 ) – (4.49 x 10 5 )

These two numbers have similar exponents Using the distributive property of multiplication; the numbers are factored out as shown below: = (6 x 10 5 ) – (4.49 x 10 5 ) = (6 – 4.49) × 10 5 Adding the coefficients and multiplying by the power of 10, we get = 1.51 × 10 5 Thus, the answer is 1.51 × 10 5

Subtract: (3.25 x 10 5 ) – (9.8 x 10 2 )

Here, the powers of the numbers are different. Thus we need to manipulate the power with a larger exponent. Using the property of exponents:  a m  x a n  = a m + n , rewriting the larger exponent 10 7 into (10 3 × 10 4 ) = (3.25 x 10 5 ) – (9.8 x 10 2 ) = (3.25 x 10 3 × 10 2 ) – (9.8 x 10 2 ) = [(3.25 x 10 3 ) × 10 2 ] – (9.8 x 10 2 ) = (3250 × 10 2 ) – (9.8 x 10 4 ) = (3250 – 9.8) × 10 2 Adding the coefficients and multiplying by the power of 10, we get = 3,240.2 × 10 2 Thus, the answer is 3,240.2 × 10 2

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Adding and Subtracting Scientific Notation Lesson Plan

Get the lesson materials.

Adding and Subtracting Scientific Notation Guided Notes with Doodles | Lesson

Ever wondered how to teach adding and subtracting numbers in scientific notation in an engaging way to your eighth-grade students?

In this lesson plan, students will learn about scientific notations and their real-life applications. Through artistic, interactive guided notes, check for understanding, a doodle & color by number activity, and a maze worksheet, students will gain a comprehensive understanding of adding and subtracting numbers in scientific notation.

The lesson culminates with a real-life example that explores how adding and subtracting numbers in scientific notation is used in practical situations.

• Standards : CCSS 8.EE.A.3 , CCSS 8.EE.A.4
• Grade : 8th Grade
• Type : Lesson Plans

Learning Objectives

After this lesson, students will be able to:

Understand the concept of scientific notation and its purpose in representing large and small numbers

Add and subtract numbers expressed in scientific notation

Recognize and explain the importance of adding and subtracting numbers in scientific notation in various fields such as science, engineering, and economics.

Prerequisites

Before this lesson, students should be familiar with:

Basic operations of addition and subtraction of integers

Understanding of place value and exponents

Colored pencils or markers

Adding and Subtracting Scientific Notation Guided Notes

Key Vocabulary

Scientific Notation

Power of 10

Coefficient

Standard Form

Introduction

As a hook, ask students why adding and subtracting numbers in scientific notation is important in real-life applications. Refer to the last page of the guided notes as well as the FAQs below for ideas.

Use the first page of the guided notes to introduce adding and subtracting numbers expressed in scientific notation. Walk through the key points of the topic, including how to add and subtract the numbers and how to rewrite the numbers in scientific notation form. Refer to the FAQ below for a walk through on this, as well as ideas on how to respond to common student questions.

Based on student responses, reteach concepts that students need extra help with. If your class has a wide range of proficiency levels, you can pull out students for reteaching, and have more advanced students begin work on the practice exercises.

Have students practice adding and subtracting numbers in scientific notation using the practice worksheet on the second page of guided notes. Walk around to answer student questions.

Fast finishers can dive into the maze activity (page 3 of guided notes) and color by number (page 4 of guided notes) for extra practice. You can assign it as homework for the remainder of the class.

Real-Life Application

Bring the class back together, and introduce the concept of real-life uses of adding and subtracting numbers in scientific notation. Use the last page of the guided notes for students to read a detailed example of adding and subtracting numbers in scientific notation form. Explain that scientific notation is commonly used in various fields of science, such as astronomy, physics, and chemistry, where extremely large or small numbers are encountered.

To illustrate the real-life application, provide the students with examples of situations where scientific notation is used generally. Some examples could include:

Astronomical Distances: In astronomy, scientists often work with incredibly large distances, such as the distance between stars or galaxies. Expressing these distances in standard form would result in numbers with many zeros. For example, the distance from the Sun to the nearest star, Proxima Centauri, is approximately 4.22 × 10^13 kilometers.

Molecules and Atoms: In the field of chemistry, scientists often deal with extremely small numbers, such as the number of atoms or molecules in a substance. For instance, a single drop of water contains approximately 3.34 × 10^22 molecules.

Earthquakes: When measuring the intensity of earthquakes, scientists use the Richter scale, which represents the magnitude of seismic waves caused by the earthquake. The Richter scale uses scientific notation to express the energy released during an earthquake. For example, a magnitude 7 earthquake releases about 2.0 × 10^15 joules of energy.

Ask the students to brainstorm other examples they can think of where scientific notation is useful in real life. Encourage discussion and allow them to share their ideas with the class.

Refer to the FAQ section for more ideas on how to incorporate real-life applications into this lesson.

Additional Self-Checking Digital Practice

If you’re looking for digital practice for adding and subtracting numbers in scientific notation, try my Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun, and a powerful tool for differentiation.

Here are some activities to explore:

Adding & Subtracting Scientific Notation Pixel Art

Additional Print Practice

A fun, no-prep way to practice adding and subtracting numbers in scientific notation is Doodle Math — they’re a fresh take on color by number or color by code. It includes multiple levels levels of practice, perfect for a review day or sub plan.

Here are some activities to try:

Operations with Scientific Notations Doodle Math Worksheets (Add, Subtract, Multiply, Divide)

What is scientific notation? Open

Scientific notation is a way to express numbers that are very large or very small. It is written as a number between 1 and 10 multiplied by a power of 10. For example, 3.4 x 10^5 represents the number 340,000.

How do you add numbers in scientific notation? Open

To add numbers in scientific notation, you need to make sure the exponents of the powers of 10 are the same. Then, you can simply add or subtract the coefficients. Finally, adjust the coefficient to make it between 1 and 10 if necessary.

How do you subtract numbers in scientific notation? Open

Subtracting numbers in scientific notation follows the same steps as adding them. Make sure the exponents of the powers of 10 are the same, subtract the coefficients, and adjust the coefficient to be between 1 and 10 if needed.

What is the purpose of using scientific notation? Open

Scientific notation is used to represent very large or very small numbers in a concise way. It makes it easier to perform calculations and work with these numbers, especially in scientific and mathematical fields.

How can I convert a number to scientific notation? Open

To convert a number to scientific notation, first identify the coefficient, which is a number between 1 and 10. Then, count the number of decimal places you need to move the decimal point to get the original number. If you move the decimal point to the left, the exponent of the power of 10 will be positive. If you move it to the right, the exponent will be negative.

What are some real-life applications of scientific notation? Open

Scientific notation is commonly used in scientific research, engineering, and astronomy. It helps represent distances between planets, the sizes of atoms and molecules, and the masses of celestial objects. It is also used to express very large or small quantities in fields such as biology, chemistry, and physics.

How does scientific notation relate to powers of 10? Open

Scientific notation uses powers of 10 to represent very large or small numbers. The exponent in scientific notation tells us how many times we need to multiply or divide the coefficient by 10 to get the original number.

Where can I find more practice problems for adding and subtracting numbers in scientific notation? Open

You can find additional practice activities (print and digital) for adding and subtracting numbers in scientific notation here . You may also consider using worksheets and activities specifically designed for practicing this skill.

Want more ideas and freebies?

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Scientific Notation

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Roodatram Kawalram

Writing numbers in scientific notation and add and subtract scientific notation

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Adding and subtracting scientific notation

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