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Scientific Notation Worksheets

Scientific notation is a smart way of writing huge whole numbers and too small decimal numbers. This page contains worksheets based on rewriting whole numbers or decimals in scientific notation and rewriting scientific notation form to standard form. This set of printable worksheets is specially designed for students of grade 6, grade 7, grade 8, and high school. Access some of them for free!

Scientific Notation - Positive Exponents

Express in Scientific Notation

Each pdf worksheet contains 14 problems rewriting whole numbers to scientific notation. Easy level has whole numbers up to 5-digits; Moderate level has more than 5-digit numbers.

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Express in Standard Notation

Students of 6th grade need to express each scientific notation in standard notation. An example is provided in each worksheet.

Both Standard and Scientific Notations

Each printable worksheet contains expressing numbers in both scientific and standard form.

Scientific Notation - Negative Exponents

Rewrite in Scientific Notation

Rewrite the given decimals in scientific notation. Move the decimal point to the left until you get the first non-zero digit. The number of steps you moved represent the power (index) of 10.

Rewrite in Standard Notation

In this set of pdf worksheets, express each number in standard notation. Easy level has indices more than -5; Moderate level has indices less than -4.

Each worksheet has ten problems expressing decimals in both standard and scientific notation.

Scientific Notation - Mixed Exponents

Convert to Scientific Notation

The printable worksheets in this section contain expressing both whole numbers and decimals in scientific notation.

Convert to Standard Notation

The exponent in each scientific notation can be either positive or negative.

This section of pdf worksheets gives the complete review in rewriting numbers in both standard and scientific notation. Both positive and negative exponents included.

Comparing Numbers in Scientific Notation

Call upon your inner math maestro as you sail through figuring out which of the given numbers in scientific notation is greater than, less than, or equal to the other.

Scientific Notation - Math Operations

Addition and Subtraction

This section reinforces the knowledge in adding and subtracting numbers in scientific notation.

Multiplication and Division

Use laws of exponents (indices) to multiply and divide the expressions. Express the final answer in scientific notation.

Simplify the Expression

Each worksheet gives the complete review in performing operations with scientific notations, making it ideal for 7th grade, 8th grade, and high school students.

Related Worksheets

» Exponents

» Logarithms

» Multiplying Decimals by Powers of Ten

» Dividing Decimals by Powers of Ten

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Home > Math Worksheets > Measurement > Scientific Notation

Scientific notation is the process of minimizing the larger value into contracted form. When we squeeze extra digits, the value will change into 10 rest to power value. Managing quite larger value, especially in mathematical terms, is not more than chewing iron pallets. But, the use of scientific notation made this problem easy, Either the value is too large or little, we can now handle it very well. How can we do it? Mathematically; you can transform the value 0.0000000056 into 5.6 x 10 -9 . For the value 5.6 x 10 -9 , the product of two numbers = 5.6 (the digit term), power value = 10 9 . We get +ve 10 rest to power value by shifting the decimal point at the right-hand side. And, we get -ve 10 rest to power value by moving the decimal point at the left-hand side. For example: In scientific notation, the value for +ve exponent is: 46600000 = 4.66 x 10 7 . And, for -ve value of the exponent will be like this; 0.00053 = 5.3 x 10 -4 . Here, the zeros of the above are place Holders. The digital term has a pair of significant figures.

When we run into very large or very small numbers scientific notation can really help you make things simpler. It allows us to leave a whole bunch of trailing zeroes out of the picture. This is sometimes called Powers of Ten notation. Scientific notation consists of two main parts the trailing non-zero digits expressed to the decimal value of the tens place and the power of ten raised to the value to express all the trailing zeroes. These worksheets explain how to read scientific notation. Activities include converting between decimal form and scientific notation, determining the correct notation based on place value, and more.

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Scientific notation worksheets, click the buttons to print each worksheet and answer key., scientific notation and powers of ten lesson.

This will show students how to write the number in scientific notation using powers of ten. A sample problem is solved.

Lesson and Practice

Students will solve for X. A sample problem is solved and two practice problems are provided.

Students will fill in the blanks to write the same numbers three ways Ten problems are provided.

Students will practice writing the numbers as indicated. Ten problems are provided.

Students will write the numbers as indicated. Eight problems are provided.

Students will write numbers in the form that is indicated. Three problems are provided.

Multiplication/Division with Scientific Notation Lesson

This worksheet explains how to treat the powers and the whole numbers as you process the operation. A sample problem is solved, and two practice problems are provided.

Students will do multiplication/division with scientific notation. Ten problems are provided.

Students will practice working with this nottations through product and quotient based operations. Ten problems are provided.

Review and Practice

The concept of working with operators and powers is reviewed. A sample problem is solved. Six practice problems are provided.

Students will demonstrate their proficiency with processing these calculations. Ten problems are provided.

Students will plow through a series of math operations that are in scientific notation. Three problems are provided, and space is included for students to copy the correct answer when given.

Place Value/Scientific Notation Lesson

A number written as an addition problem is called expanded form. Expanded form is a way to break up a number to represent the value of each digit in the number. In other words, the expanded form is the method of pulling a number apart and expressing it as a sum of the value of each digit.

Normal form of any number is the form in which we write the digits to make a single digit. All the digits which were represented in multiplication form or expanded from shows their respective positions. To make the number in normal form we will add all the numbers.

Expanded Form Worksheet

Students will write the numbers in expanded form. Ten problems are provided.

Normal Form Practice

Students will write the numbers in normal form. Ten problems are provided.

Place Value Drill

Students will identify the place value of the underlined digit. Eight problems are provided.

Form Warm Up

Students will write each expression in normal form. Three problems are provided.

Decimal Skill Lesson

This worksheet explains how to write values in decimal form for an expression. A sample problem is solved.

Students will convert values from scientific notation to decimal form. A sample problem is solved and two practice problems are provided.

We show you how to focus on the individual terms in this form of notation. Ten problems are provided.

Students will practice writing values in decimal form. Ten problems are provided.

Students will get more work in on this skill. Eight problems are provided.

This sheet works well for introducing the skill. Three problems are provided.

Scientific Notation Basic Skills Worksheet

Students will practice basic skills of converting values to normal form. Ten problems are provided.

Basic Skills Practice

More work with turning values into a different form. Ten problems are provided.

Intermediate Skills Worksheet

Students will demonstrate rewriting all these value in standard form. Ten problems are provided.

Intermediate Skills Check

We will see how you do with more advanced values here. Ten problems are provided.

Intermediate Skills Drill

Students will use intermediate skills with converting values in scientific notation. Ten problems are provided.

Working with Scientific Notation Lesson

This worksheet explains how to place values from an expression in decimal form. A sample problem is solved.

Students will get some more practice with the basic concept we are working on. A sample problem is solved and two practice problems are provided.

Take these values and change how they appear. Ten problems are provided.

You will get a better idea of where you stand with this concept as you drive through all these problems.

Students will write transfer value in scientific notation to decimal form for an expression. Ten problems are provided.

Use these three problems to review the skill as an entire group.

Converting Between Standard Form and Scientific Notation Lesson

This worksheet explains how to convert between standard form and scientific notation. A sample problem is solved, and two practice problems are provided.

You will go in both directions on this sheet. Ten problems are provided.

Get more work in on both the skills we have learned so far. Ten problems are provided.

Both transitions are reviewed over this selection of exercises. A sample problem is solved. Six practice problems are provided.

Students will demonstrate their proficiency with the skills we have seen so far. Ten problems are provided.

Get your mind in the right rotation here. Three problems are provided, and space is included for students to copy the correct answer when given.

Write in Scientific Notation Lesson

This worksheet explains the anatomy of these types of problems. You are shown a strategy to use often to tackle these types of exercises. A sample problem is solved.

By this point, you should be pretty solid on this skill. A sample problem is solved and two practice problems are provided.

We start to use our basic algebra skills with these ten problems that are provided.

As basic as it gets with this skill. Ten problems are provided.

Remember to count all of the places as you progress through the numbers. Eight problems are provided.

Students will develop proficiency with this skill. Three problems are provided.

Scientific Notation (Writing) Lesson

This worksheet explains how to use scientific notation in writing. A sample problem is solved, and two practice problems are provided.

You will use scientific notation to express decimal and whole values. Ten problems are provided.

Students will practice converting values to scientific notation. Ten problems are provided.

The concept of how to use scientific notation to express values is reviewed. A sample problem is solved. Six practice problems are provided.

Students will demonstrate their proficiency with scientific notation in their writing. Ten problems are provided.

Students will use scientific notation to change the format of a series of values. Three problems are provided, and space is included for students to copy the correct answer when given.

Basic Skills Writing in Scientific Notation Worksheet

Students will practice basic skills with writing in scientific notation. Ten problems are provided.

Students will demonstrate their basic skills with scientific notation. Ten problems are provided.

Intermediate Skills Writing in Scientific Notation Worksheet

These exercises are a bit more complex. Ten problems are provided.

Students will demonstrate their use of this skill.

Notation Drill

Students will gain proficiency with scientific notation. Ten problems are provided.

Math Collage

Students will use mathematics to create a collage. Directions are provided.

Introducing the Concept

This worksheet explains the basics of scientific notation. Twenty problems are provided.

Calculations with Scientific Notation

This worksheet explains how to do operations when using scientific notation. Ten problems are provided.

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Scientific Notation

The worksheets on this page can be used to teach or review scientific notation.

Level: Basic Whole Numbers

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Level: Intermediate Includes Decimals

Level: advanced decimals & negative exponents.

These worksheets and task cards can be used for teaching students about exponents.

Practice finding the reciprocals of fractions and mixed numbers.

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Scientific Notation Worksheets (Standard to Scientific Notations)

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 convert from Standard Notation (Real Notation) to Scientific Notation.

How to convert from Standard Notation to Scientific Notation?

There are three sets of converting from Standard to Scientific Notation worksheets.

• Standard to Scientific Notation (positive exponents).
• Standard to Scientific Standard Notation (negative exponents)
• Standard to Scientific Standard Notation (positive & negative exponents).

These are the steps to convert a number from standard notation (real notation) to scientific notation:

• Move the decimal point so that there is one digit before the decimal point.
• Count the number of places that you moved point. This will be the exponent in the scientific notation. If you moved the decimal point to the left then the exponent is positive. If you moved the decimal point to the right then the exponent is negative.
• Express the number as a coefficient multiplied by 10 raised to the power of the exponent.

Example: Convert the number 67,000 to scientific notation.

• Move the decimal point after the first nonzero digit. From 67000. to 6.7000
• We have moved the decimal point 4 places to the left. This means the exponent will be 4.
• 67,000 = 6.7 × 10 4 (in scientific notation)

Example: Convert the number 0.00004321 to scientific notation.

• Move the decimal point after the first nonzero digit. From 0.00004321 to 4.321
• We have moved the decimal point 5 places to the right. This means the exponent will be -5.
• 0.00004321 = 4.321 × 10 -5 (in scientific notation)

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

More Scientific Notation Worksheets

Printable (Answers on the second page.) Scientific Notation Worksheet #1 (positive exponents) Scientific Notation Worksheet #2 (negative exponents) Scientific Notation Worksheet #3 (positive or negative exponents)

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Scientific Notation Conversion

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Scientific Notation (A)

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Free Printable Scientific Notation worksheets

Discover a collection of Free Printable Math Scientific Notation worksheets, perfect for math teachers and students alike. Explore various exercises to enhance understanding and mastery of this essential mathematical concept.

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Explore printable Scientific Notation worksheets

Scientific Notation worksheets are an essential tool for teachers who aim to enhance their students' understanding of Math and Number Sense. These worksheets provide a structured and engaging way for students to practice converting numbers between standard form and scientific notation, as well as performing operations with numbers in scientific notation. By incorporating these worksheets into their lesson plans, teachers can ensure that their students develop a strong foundation in this important mathematical concept. Furthermore, these worksheets can be easily adapted to cater to different grade levels and learning abilities, making them a versatile resource for any classroom.

Quizizz is an innovative platform that offers a wide range of educational resources, including Scientific Notation worksheets, to support teachers in delivering effective and engaging Math and Number Sense lessons. With Quizizz, teachers can create interactive quizzes and games that not only test students' understanding of scientific notation, but also help to reinforce key concepts and develop problem-solving skills. In addition to worksheets, Quizizz also offers a variety of other resources such as flashcards, videos, and interactive lessons, allowing teachers to create a comprehensive and dynamic learning experience for their students. By incorporating Quizizz into their teaching strategies, educators can ensure that their students are well-equipped to tackle the challenges of Math and Number Sense at any grade level.

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SCIENTIFIC NOTATION

Home > Algebra  > Scientific Notation

Scientific Notation worksheets here teach you the best way to express very large numbers and very small numbers. It is represented conveniently using exponents. The numbers are shortened (a number between 1 to 10) and multiplied in the power of 10. The powers for very large numbers are expressed using positive exponents and very small numbers using negative exponents. In these worksheets , learn to express standard numbers in scientific form and scientific numbers in standard form. Also scientific notation Addition, Subtraction, Multiplication, and Division worksheets have been prepared for advanced learning.

SCIENTIFIC NOTATION WORKSHEETS

RELATED ALGEBRA TOPICS   :    Order of Operations ,  Forming algebraic expressions and translating phrases

Let us learn how to express the numbers

The mass of earth is 5,970,000,000,000,000,000,000,000 kg. Such large numbers are represented using exponents. We represent it as 5.97 x 10 24

Thus 10 is base here and 24 is the power in 5.97 x 10 24

Lets us see how to represent it. Look into the number.

Place a decimal point at the end of the number. Now move the decimal 24 places to the left, such that you place the decimal point imediately after the first digit of the given number.

What does this expression 5.97 x 10 24 mean?

5.97 x 1000000000000000000000000 (24 zeros)

5.97 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10.

Eg. Negative Integer

The size of a atom is 0.0000000008 m. We represent it as 8 x 10 -10 m. Here you need to move the decimal point10 places right.

What does the expression 8 x 10 -10 mean?

8 x 0.0000000001

8 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1

As the exponent decreases by 1, the value becomes one- tenth of the previous value.

Generally mathematicians, scientists and engineers deal with very large and very small numbers on daily basis. They also do exponent addition, subtraction, multiplication, and division. Here is an example for each operation.

When you add two or more exponents, the powers should be made equal first. Its is always better to convert the smaller power to the highest power.

Just like addition, when you subtract exponents, the powers should be the same.

When you multiply two exponents, just add the powers. a m x a n = a m+n , where m and n are natural numbers.

When you divide two exponents, subtract the powers. a m / a n = a m-n , where m and n are natural numbers.

Positive Exponents - To Scientific - Upto 5

• Worksheet #1
• Worksheet #2
• Worksheet #3

Positive Exponents - To Scientific - Upto 10

Positive Exponents - To Standard - Upto 5

Positive Exponents - To Standard - Upto 10

Negative Exponents - To Scientific - Upto 5

Negative Exponents - To Scientific - Upto 10

Negative Exponents - To Standard - Upto 5

Negative Exponents - To Standard - Upto 10

Addition / Subtraction

Multiplication / Division

Match the following

Express in Scientific form - Word Problems

Word Problems

Frequently Asked Questions!!

1) what is scientific notation in math.

Scientific notation is an easy way to express very large and very small numbers using exponents. Positive exponents are used to represent large numbers and negative exponents for small numbers. Eg. The mass of earth is 5,970,000,000,000,000,000,000,000 kg. It is represented as 5.97 x 10^24

2) Define the three parts of scientific notation?

Consider this number 786,000,000,000. Expressing it in scientific form as 7.86 x 10^11 7.86 is the number. 10 is the base. 11 is the exponent.

3) How to convert scientific notation into standard form?

First make a note of the power. Also make a note of the decimal number. If there are 2 numbers after the decimal dot, subtract if from the power. This difference is the number of zeros to be added. Now write the number with zeros. Eg. 1.46 x 10^15 Power- 15 Digits after decimal dot= 2 Difference= 13 Therefor the standard form is 1,460,000,000,000,000 (Number and 13 zeros)

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Scientific Notation

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Scientific Notation Worksheets

February 13, 2024

3 minutes read

One way to simplify the presentation of big or tiny numbers is using scientific notation. Using scientific notation is one approach to making these figures more straightforward. Using the multiplication method of single-digit integers and then increasing to the power of the relevant exponent, scientific notation allows students to express very large or small numbers.

Scientific notation can appear complex to kids when explained verbally, so educational resources like YouTube videos and other online resources are often needed.

Keep reading this article to know more about the scientific notation worksheets to make math easier.

All About The Scientific Notation Worksheets

Scientific notation requires the shift of the decimal point to the right or left to form a whole number between one and ten, omitting 10. When you shift the decimal point to the right, your exponent equals minus the number of places transferred to the negative side.

When students in 8th grade use the scientific notation math worksheets, they can get introduced to the standard way the concept is expressed: a × 10b; 1 ≤ a < 10. In the expression, “a” stands for the coefficient, and “b” stands for the exponent. In this case, the coefficient is a left-to-right integer with a mantissa added. The significant digits to the right of the decimal point are called the mantissa.

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How to use the scientific notation worksheet.

By using scientific notation worksheets and answers, students may express 567,000 easily. In this example, the non-zero digits of the number are 5, 6, and 7. The decimal representation of these digits is a number between one and ten. This yields a representation of 5.67 for 567,000.

With the scientific notation 8th grade common core worksheets, the next step is to find the necessary power of 10 to get the value back to its original state. To do this, we see that to get 567,000, we need to shift the decimal point five places to the right. Therefore, 10^5 is the power of 10.

So, 567,000 is written as (5.67 \times 10^5) in scientific notation. In a bid to make the original numerical value more compact, this scientific notation multiplies the decimal component (5.67) by 10, raised to the power of 5, to get the new value.

Why Should You Use a Scientific Notation Worksheets

Math is complex and challenging, according to most pupils all across the globe, as they are scared off by the very mention of the topic. Although students may find it challenging, professionals have developed tactics and approaches like using worksheets to make things simpler for everyone. Now, students can use math scientific notation worksheets to streamline the process of understanding scientific notation. 

Scientific notation printable worksheets are helpful because they reduce the complexity, ease of use, and potential for mistakes in mathematical operations.

As a seasoned educator with a Bachelor’s in Secondary Education and over three years of experience, I specialize in making mathematics accessible to students of all backgrounds through Brighterly. My expertise extends beyond teaching; I blog about innovative educational strategies and have a keen interest in child psychology and curriculum development. My approach is shaped by a belief in practical, real-life application of math, making learning both impactful and enjoyable.

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Scientific Notation Worksheets

What is Scientific Notation? There are times when we have to deal with numbers that are too big or too small to write and can take up a lot of our time. It is where we can use scientific notations. These notations are a part of mathematical language, which makes problem-solving simpler and much more convenient. Scientific notations are a way we can easily write a number that is too big or small as a product of a real number and power of 10. The general form of a number written in scientific notation is; a × 10 b . Here; a is the coefficient and b is the exponent. The co-efficient is a non-zero value and is a combination of an integer, decimal point, and a mantissa. The mantissa is a term that many students are unaware of. It is the digits that lie on the right side of decimal and hold significant value. Consider the number 0.000000000000162 | When you are writing down this number, there are chances that you miss out one or two zeros on the right side of the decimal and it can expose your calculations to errors. Therefore, you can write it in a simpler manner; 1.62 × 10 -14 When you have to move the decimal to the right-hand side of the decimal, the exponent becomes negative, and when the decimal moves towards the left, the exponent becomes positive. Get started with powers of ten and then work your way towards using this form of notation in our word problems. Did you know that scientists account for 90% of the usage of this form of notation, I guess that was a no brainer!

Scientific Notation Worksheet Categories

• Powers of Ten and Scientific Notation - We show how these forms of notation are used to represent very large and very small numbers. This can help us communicate these difficult to quantify values very quickly and with ease.
• Scientific Notation Word Problems - These are practical problems that you will find in most High School science lab environments. You will also see this skill come up in many different advanced math programs.
• Scientific Notation Addition and Subtraction - Yes, there are a few tricks to calculating these quickly. Make sure that you have a good handle on the concept of place value and the meaning of a base ten number. That will come in very helpful.
• Scientific Notation Multiplication and Division - This is one of the tougher section for students that are studying this topic. When students work with these values and using product operations, they do not have much trouble. As the kids move up to quotients, in this environment, it can get difficult quickly.

Where Is Scientific Notation Used in The Real World?

This is a very common question that many students will have. It is important to see value in the things that you learn. It helps motivate you and keep you focused. The first use of scientific notation is not well documented, but it become more and more common place as scientific research grew. In the nineteenth century, it started really to bubble up and work its way to become the scientific standard by the twentieth century. As research begins to explore now layers of the universe and microscopic regions of our world, this form of notation is not only needed, but required in order to communicate the results of experiments as well to explain the movement of such matter. Things in the universe are very large and the distances between them are very far apart. To convey these dimensions with data we have to use immense values. For example, the planet Jupiter is enormous. If you were to combine all the other planets in the Milky Way Galaxy, Jupiter would still be two and half times their mass. This is because Jupiter's mass is 1.9 x 10 27 kilograms. If we were to remove the notation we would be working with the value as: 1,900,000,000,000,000,000,000,000,000. I added the commas for my own sanity. All known elements are made up of protons, neutrons, and electrons. Protons and neutrons are made up of even tinier building blocks called quarks. A quark is 0.43 x 10 -16 centimeters in size. That is forty-three billion-billionths of a single centimeter. If we were to remove the scientific notation the value would be: 0.000000000000000043. Simply be using this way to express values, think of all of the paper we are saving the world. Needless to say, if you decide on a career in research, of any kind, you can expect to make it a habit of using scientific notation on a daily basis.

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