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## Scientific Notation – Working With Exponents

Scientific notation is a method of writing very large or very small numbers in decimal form. The method is used by scientists, engineers, and mathematicians. Scientific notation is also called standard form, standard index form, or scientific form. Examples of large numbers written in scientific notation include Avogadro’s number (6.022 x 10 23 ) and the speed of light (3.0 x 10 8  m/s). An example of a small number written using scientific notation is the electrical charge of an electron (1.602 x 10 -19  Coulombs).

## Scientific Notation Basics

In scientific notation, numbers are written in two parts using the form m  × 10 n where m is any real number and n is an integer exponent . The real number is called the mantissa or significand, while the exponent is called the mantissa.

There are multiple ways to write any real number in scientific notation. For example: 250 = 2.5 x 10 2  = 25 × 10 1  = 250 × 10 0 = 2500 x 10 -1 0.014 = 1.4 x 10 -2 = 14 x 10 -3 = 0.0014 x 10 1

Numbers are usually reported using normalized scientific notation or the standard form, where m is a decimal number greater than or equal to 1 but less than 10. Examples of numbers written in the standard form include 2.5 x 10 2 and 1.4 x 10 -2 . Even though you may report numbers this way, it’s important to know how to convert to scientific notation using other exponents so that you can perform calculations with two numbers both written in scientific notation.

To write a large number in standard form, move the decimal point to the left until only one digit remains to the left of the decimal point. Large numbers always have positive exponents. For example: 3,454,000 = 3.454 x 10 6 For small numbers, move the decimal point to the right until only one digit remains to the left of the decimal point. Small numbers always have negative exponents in standard form. For example: 0.0000005234 = 5.234 x 10 -7

## Scientific Notation Worksheet

Practice writing numbers in scientific notation and converting them from scientific notation into decimal form. The worksheet and answer key are in PDF format for downloading and printing. Otherwise, simply right-click and save the image file.

• Scientific notation worksheet [ PDF worksheet ] [ Answer key ]

## Addition and Subtraction Using Scientific Notation

Handle addition and subtraction the same way:

• Write the two numbers in scientific notation. First make certain the two numbers have the same exponent as each other. If they do not, convert one of them to match the other. It doesn’t matter which one you convert.
• Add or subtract the first part of the numbers, leaving the exponent portion unchanged.
• Report the number in the standard form of scientific notation.

Examples: (1.1 x 10 3 ) + (2.1 x 10 3 ) = 3.2 x 10 3 (5.3 x 10 -4 ) – (2.2 x 10 -4 ) = (5.3 – 1.2) x 10 -4  = 3.1 x 10 -4

## Multiplication and Division With Scientific Notation

You don’t need the exponents to be the same for multiplication and division.

• Multiply (or divide) the first part of the two numbers.
• For multiplication, add the exponents. For division, subtract the exponents.
• Convert the answer to standard form.

Multiplication Example

(2.3 x 10 5 )(5.0 x 10 -12 ) =

Multiply 2.3 and 5.3 to get 11.5. Add the exponents to get 10 -7 . At this point, the answer is:

11.5 x 10 -7

You want to express your answer in standard scientific notation, which has only one digit to the left of the decimal point, so the answer should be rewritten as:

1.15 x 10 -6

Division Example

(2.1 x 10 -2 ) / (7.0 x 10 -3 ) = 0.30 x 10 1  = 3.0 x 10 -1 Be sure to watch your significant figures !

## Using Scientific Notation on Your Calculator

A basic calculator can’t handle scientific notation. To use it, you need a scientific calculator. The method to enter numbers varies by manufacturer and model. To enter in the numbers, look for a ^ button, which means “raised to the power of” or else y x  or x y , which means y raised to the power x or x raised to the y, respectively. Another common button is 10 x , which makes scientific notation easy. The way these button function depends on the brand of calculator, so you’ll need to either read the instructions or else test the function. You will either press 10 x  and then enter your value for x or else you enter the x value and then press the 10 x  button. Test this with a number you know, to get the hang of it.

Calculator brands handle order of operations differently from one another. Ideally, exponent operations come before multiplication and division, which come before addition and subtraction. But, it’s a good idea to use parentheses, when available, to force the order of operations. Practice entering simple equations (or read the manual) to make certain calculations are carried out correctly.

Some calculators and most computers use a key labeled E, EE, EXP (for exponent), or EEX (for enter exponent) because their display cannot display superscript exponents. The capital letter E is used to distinguish scientific notation from the natural logarithm e. Usually, scientific notation is entered using the format m E n to signify m x 10 n . Certain calculators, such as the popular TI-84, offer options to display values using E notation or superscripts.

• Lide, David R. (ed.). (June 6, 2000). Handbook of Chemistry and Physics (81st ed.). CRC. ISBN 978-0-8493-0481-1.
• McCalla, J.; Edwards, C.C. (2013). “ How to Work in Scientific Notation on the TI-84 Plus Calculator .” TI-84 Plus Graphing Calculator for Dummies (2nd ed.). ISBN: 9781118592151
• Mohr, Peter J.; Newell, David B.; Taylor, Barry N. (July–September 2016). “CODATA recommended values of the fundamental physical constants: 2014”. Reviews of Modern Physics . 88 (3): 035009. arXiv:1507.07956. doi: 10.1103/RevModPhys.88.035009

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Scientific notation.

Develop skills in converting to and from scientific notation

This worksheet provides practice in converting large and decimal values between real and scientific notation. This skill is important for almost any science course, but especially chemistry and physics where either extremely large or extremely small values must be handled.

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## Scientific Notation

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

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## Level: Intermediate Includes Decimals

Level: advanced decimals & negative exponents.

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• Scientific Notation

## 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.

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

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.

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## Scientific Notation Worksheets

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## Worksheet # 1 - Answers on 2nd Page of PDF

For Example: 3,800 = 3.8 × 10 3

7.68 × 10 5 = 768,000

These worksheets requiring converting to and from the use of scientific notations.

## Worksheet # 2 - Answers on 2nd Page of PDF

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## Scientific Notation Worksheets

Scientific notation worksheets help students understand that scientific notation is a way in which numbers are expressed that are too large or too small. These numbers can be conveniently written in decimal form. It is also referred to as standard index form, scientific form, or standard form in the UK.

## Benefits of Scientific Notation Worksheets

Scientific notation worksheets help students get familiar with the concept of expressing very large or very small numbers in exponential form. This can be extremely beneficial in conveying different quantities in the quickest way possible, thus helping students to solve complex problems in no time. These math worksheets boost problem-solving skills of a student and help them understand the topic with ease. These worksheets can help students visualize concepts. Visual simulations in these worksheets help students get a crystal clear understanding of the topic.

Scientific notation worksheets not just help students mathematically but also help them deal with real-life problems, thus boosting the problem-solving skills of students. These worksheets also help in boosting the reasoning and logical skills of students.

## ☛ Check Grade wise Scientific Notation Worksheets

• 8th Grade Scientific Notation Worksheets

## Scientific Notation (A)

Welcome to The Scientific Notation (A) Math Worksheet from the Number Sense Worksheets Page at Math-Drills.com. This math worksheet was created or last revised on 2008-08-25 and has been viewed 10 times this week and 731 times this month. It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math.

Teacher s can use math worksheets as test s, practice assignment s or teaching tool s (for example in group work , for scaffolding or in a learning center ). Parent s can work with their children to give them extra practice , to help them learn a new math skill or to keep their skills fresh over school breaks . Student s can use math worksheets to master a math skill through practice, in a study group or for peer tutoring .

Use the buttons below to print, open, or download the PDF version of the Scientific Notation (A) math worksheet . The size of the PDF file is 11669 bytes . Preview images of the first and second (if there is one) pages are shown. If there are more versions of this worksheet, the other versions will be available below the preview images. For more like this, use the search bar to look for some or all of these keywords: numeration, number, sense, mathematics, math .

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## Scientific Notation Worksheets

• Pre-Algebra >

Our free, printable scientific notation worksheets proclaim that there's a rapid mathematical promotion on the horizon. Structured to accommodate a comprehensive practice session, it covers interpretation, expression, and comparison of numbers in scientific notation, alongside all four basic arithmetic operations in every possible combination.

Our pdf scientific notation worksheets are recommended for math enthusiasts in grade 8.

Scientific Notation of Large Numbers Worksheets

Crank up your practice with these worksheets that emphasize large numbers, and you’ll see no number is too daunting for you to express in its scientific or standard notation.

Scientific Notation of Small Numbers Worksheets

Watch the child put their heart and soul into scientific notation of small numbers, observing the number of zeros and the whereabouts of the decimal point in these worksheets.

Express in Scientific Notation - Easy

Tower above your peers in the 8th grade with these scientific notation worksheets pdf. Make the most of math time by quickly expressing these numbers in scientific notation.

Express in Scientific Notation - Moderate

Invigorate practice of scientific notation through these engaging exercises that feature numbers that are a little more challenging for kids to express in scientific notation.

Reading Numbers in Scientific Notation - Easy

Put your scientific notation prowess to the test by writing numbers in standard notation in these printable reading numbers in scientific notation worksheets for grade 8.

Reading Numbers in Scientific Notation - Moderate

Take review sessions a notch higher with these moderate-level mixed practice exercises for 8th grade, where you write a range of numbers in standard notation.

Convert between Standard and Scientific Notation - Easy

Traverse through the numbers and change them to standard or scientific notation in these pdf worksheets on converting between standard and scientific notation.

Convert between Standard and Scientific Notation - Moderate

Stay on top of your scientific notation game and show off your mathematical mastery by making effortless transitions from scientific to standard notation and vice versa.

Addition and Subtraction with Scientific Notation Worksheets

Tighten your grasp on scientific notation calculations and complete with gusto the assortment of addition and subtraction problems on numbers in scientific notation.

Multiplication and Division with Scientific Notation Worksheets

Prove you're light years ahead of your peers with our printable scientific notation worksheets, answering multiplication and division problems on numbers in scientific notation.

Operations with Scientific Notation Worksheets

March toward the pinnacle of scientific notation with these worksheets on scientific notation calculations involving varying combinations of the fundamental operations.

Comparing Numbers in Scientific Notation - Easy

Quick deciphering of scientific notation is key as grade 8 students find which number is bigger or smaller than or equal to the other in these printable comparing numbers in scientific notation worksheets.

Comparing Numbers in Scientific Notation - Moderate

Radiate confidence as you ascertain which of the given numbers is greater than, less than, or equal to the other, ensuring both sides are in scientific notation first.

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Home » Worksheets » Simplify Math with These Best 10 Scientific Notation Worksheets

## Simplify Math with These Best 10 Scientific Notation Worksheets

Scientific notation can be difficult for your class to understand when you first introduce it, so having some scientific notation worksheets on hand can make it easier. If you struggle to create your own worksheets, ready-made worksheets can be a great option. We have rounded up our favorite scientific notation worksheets for you to choose from.

What to look for in scientific notation worksheets, 10 best scientific notation worksheets, where to find high-quality worksheets online by, teach simple – high-quality teaching resources for a low monthly cost, final thoughts.

To help your class consolidate their knowledge of scientific notation, the key is practice, practice, practice! The best worksheets are, therefore, ones that have plenty of examples for them to try. The worksheets below revise knowledge of converting both ways – to scientific notation and back to standard notation. As your class advances through the unit, you will be looking for worksheets that incorporate addition , subtraction, multiplication, and division with standard notation, and we have included examples of these too.

Most importantly, you want your class to be engaged and enjoying the lesson, so a worksheet that can make scientific notation fun will be the best option.

## Scientific Notation: Converting To and From & Estimating By The Math Cafe

This in-depth activity pack introduces your class to scientific notation. It includes notes for introducing the concept, followed by practice problems converting to and from scientific notation. Pupils then move on to estimating in scientific notation, with notes and practice problems provided. Finally, there are multiple-choice questions and an answer key. Suitable for Grade 8.

## Scientific Notation Worksheets By Math Worksheets 4 Kids

These worksheets from Math Worksheet 4 Kids have a variety of activities to test your class’s skills. Aimed at Grades 6-8, the activities include changing from whole numbers to scientific notation, changing from scientific to standard notation, and comparing which number is greater. All worksheets come in easy or moderate levels, though the moderate ones are not free of charge.

## Scientific Notation Worksheet By Liveworksheets

This interactive worksheet contains a variety of problems for students to work through, including writing scientific notation, converting from scientific notation to standard form, as well as adding and subtracting. Suitable for Grades 8-10, students can have their work marked automatically, or they can send it to you for review.

## Scientific Notation Consolidation Worksheet By Math Drills

This simple worksheet from Math Drills is a handy resource to help your middle school class consolidate their skills in scientific notation. It contains 20 questions that require students to convert between scientific and standard notation. It also includes an answer key to allow for peer marking.

## Operations in Scientific Notation Worksheet By The Math Cafe

This extensive resource from Teach Simple is an excellent way to improve and consolidate your class’s ability to work with scientific notation. Suitable for Grades 8 and above, these activities involve adding and subtracting in scientific notation and multiplying and dividing in scientific notation. There is a partner practice activity and some test practice questions as well.

## Interactive Scientific Notation Worksheet By Liveworksheets

This interactive worksheet from Live Worksheets can be completed as a whole-class activity using a smart board, or students can take part individually on their electronic devices. The worksheet contains 16 questions requiring conversion either from standard to scientific notation or the reverse. Suitable for Grade 8 upward.

## Scientific Notation Bundle By Sample Templates

This comprehensive bundle from Sample Templates contains nine different worksheets to test your class’s knowledge of scientific notation. It includes converting to and from scientific notation, adding and subtracting, multiplying and dividing, as well as comparing numbers. A great resource to use as homework exercises or to revise before an assessment.

## Interactive Scientific Notation Practice Worksheet By Liveworksheets

This activity from Live Worksheets contains some good practice questions to use after you introduce the concept of scientific notation to your class. Students start by identifying which terms are correctly written in scientific notation before converting to and from scientific notation. It can be done as an electronic worksheet or printed as a PDF.

## Scientific Notation Revision Exercise By Liveworksheets

This worksheet makes an excellent revision activity to prepare for an assessment. The worksheet starts with a thorough explanation of converting to and from scientific notation and goes on to test a number of different skills, including working out the power of ‘n’ in various examples.

## Scientific Notation Quiz By The Math Cafe

This quiz from Teach Simple is the perfect way to revise with your class for an upcoming assessment. The quiz is available in two different forms – printable as a PDF or a link to use in Google Forms. Using the Google Forms version means the quiz will be automatically graded, saving you time on marking!

Finding worksheets online is easy – finding high-quality worksheets that suit your needs is a more difficult task. It could take so much time to trawl through hundreds of poor-quality resources before finding something suitable, you would often be quicker creating the materials yourself.

Paid-for resources are often much higher quality, but paying individually for every worksheet or activity will soon add up,  and websites often only show you a screenshot of the materials before you commit, which could result in you paying for something that is not the quality you need.

Teach Simple is the solution you have been looking for. For an affordable monthly fee, you can have access to tens of thousands of high-quality materials created by teachers, including lesson plans , worksheets, ebooks, and more. Your monthly subscription gives you access to unlimited downloads, and 50% of your fee goes straight to the contributing teachers, meaning you can support your fellow teachers.

The site is easy to use, and you can filter resources by subject, grade, or activity type. Sign up for our free 30-day trial today to see the value for yourself.

Scientific notation worksheets are a great resource to help you introduce the topic to your class. Teach Simple is the perfect place to access these and other math worksheets to make your lessons fun and engaging. Sign up today and take the stress out of planning math lessons this term.

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Elaine T. is a teacher with 17 years of experience teaching 11-18 year-olds in Scotland, UK.

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1. PDF Writing Scientific Notation

Title: Writing Scientific Notation Author: Eleanor Hodby Created Date: 1/17/2021 6:19:19 PM

2. PDF Scientific Notation Worksheet

Scientific Notation Part A: Express each of the following in standard form. 1. 5.2 x 103 5. 3.6 x 101 2. 9.65 x 10-4 2 6. 6.452 x 10 3. 8.5 x 10 ... Scientific Notation Worksheet Author: John Bergmann and Jeff Christopherson Subject: Chemistry Keywords: scientific notation

3. PDF Scientific Notation, Metric System, & Unit Conversion Review Worksheet

Physics 151 Scientific Notation, Metric System, & Unit Conversion Review Worksheet Scientific Notation Rewrite the following numbers in scientific notation, in simplest form. Include units. Use appropriate significant figures! Altitude of summit of Mt. Ka'ala (highest point on O'ahu): 4020 ft =

4. PDF Scientific Notation and Significant Figures

SCIENTIFIC NOTATION AND SIGNIFICANT FIGURES WORKSHEET SCIENTIFIC NOTATION A digit followed by a decimal and all remaining significant figures and a power of 10 is in scientific notation. Q1. Consider the following values. 6.7 x 102 36 x 104 π x 107 2 x 107.61 4 x 10 36 7.61 x 100 0.67 x 103 382 -5.24 x 10-8 4/3 x 105 7 x 10π

5. PDF Scientific Notation Worksheets for Students

Scientific Notation Worksheets for Students Author: Scientific Notation Worksheets for Students Subject: Scientific Notation Worksheets for Students Keywords: Scientific Notation Worksheets for Students Created Date: 10/30/2006 11:15:16 AM

6. Worksheet 1

Scientific Notation/Significant Figures 1. Convert each of the following into scientific notation. 2. Determine the number of significant figures in each of the following: 3. Convert each into decimal form. 4. Calculate the following. Give the answer in correct scientific notation. a) 4.53 x 105 b) 1913.0 + 2.2 x 106 - 4.6 x 103

7. 1.2: Scientific Notation and Order of Magnitude

Scientific notation means writing a number in terms of a product of something from 1 to 10 and something else that is a power of 10. In scientific notation all numbers are written in the form of [Math Processing Error] a ⋅ 10 b (a times ten raised to the power of b). Each consecutive exponent number is ten times bigger than the previous one ...

8. Physics 102: Scientific Notation and Metric Conversions

Physics 102: Scientific Notation and Metric Conversions. Instructions. Before viewing an episode, download and print the note-taking guides, worksheets, and lab data sheets for that episode, keeping the printed sheets in order by page number. During the lesson, watch and listen for instructions to take notes, pause the video, complete an ...

9. Browse Printable Scientific Notation Worksheets

Sort by Scientific Notation Worksheet Adding and Subtracting Numbers in Scientific Notation Worksheet Operations With Numbers in Scientific Notation Worksheet Numbers in Scientific Notation Worksheet Scientific Notation Handout Worksheet Multiplying and Dividing Numbers in Scientific Notation Worksheet Compare Numbers in Scientific Notation

10. Scientific Notation

In scientific notation, numbers are written in two parts using the form. m × 10 n. where m is any real number and n is an integer exponent. The real number is called the mantissa or significand, while the exponent is called the mantissa. There are multiple ways to write any real number in scientific notation.

11. Scientific Notation Handout

This one-page reference worksheet features an explanation of what scientific notation is, several examples of numbers in scientific notation and standard form, and a demonstration on how to convert between scientific notation and standard form. Students can use this reference sheet to help them when they are converting between scientific ...

12. Scientific Notation

Develop skills in converting to and from scientific notation. This worksheet provides practice in converting large and decimal values between real and scientific notation. This skill is important for almost any science course, but especially chemistry and physics where either extremely large or extremely small values must be handled.

13. Scientific Notation Worksheets

This worksheet requires students to use decimals in their scientific notation numbers. 6th through 8th Grades View PDF Level: Advanced Decimals & Negative Exponents Sci. Notation Questions (Advanced) Answer the questions by converting numbers to and from scientific notation. 6th through 8th Grades

14. Scientific notation (practice)

Express this number in scientific notation. 0.3643. Stuck? Review related articles/videos or use a hint. Report a problem. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for ...

15. Scientific notation word problems (practice)

Scientific notation word problems. Google Classroom. You might need: Calculator. Light travels 9.45 ⋅ 10 15 meters in a year. There are about 3.15 ⋅ 10 7 seconds in a year. How far does light travel per second?

16. Scientific Notation Worksheet

Scientific Notation. I. Powers of Ten worksheet: Express the following powers of ten in "normal notation", for example 1000: 1) 104= 2) 107= 3) 1017= 4) 10-1= 5) 10-4= 6) 10-12= Express the following numbers as powers of ten. 7) 10 = 8) 100,000 = 9) 1,000,000,000,000,000,000 = 10) 0.001 = 11) 1 = 12) 0.000000001 =

17. Scientific Notation Worksheets

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.

18. Pre-Algebra Worksheets, Scientific Notation

Worksheet # 1 - Answers on 2nd Page of PDF. Worksheet # 1. D.Russell. Print Worksheet and Answers. For Example: 3,800 = 3.8 × 10 3. OR. 7.68 × 10 5 = 768,000. These worksheets requiring converting to and from the use of scientific notations. 02.

19. Scientific Notation Worksheets

Scientific notation worksheets help students get familiar with the concept of expressing very large or very small numbers in exponential form. This can be extremely beneficial in conveying different quantities in the quickest way possible, thus helping students to solve complex problems in no time.

20. Scientific Notation (A)

Welcome to The Scientific Notation (A) Math Worksheet from the Number Sense Worksheets Page at Math-Drills.com. This math worksheet was created or last revised on 2008-08-25 and has been viewed 64 times this week and 635 times this month. It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math.

21. Scientific Notation Worksheets

Scientific Notation Worksheets. Our free, printable scientific notation worksheets proclaim that there's a rapid mathematical promotion on the horizon. Structured to accommodate a comprehensive practice session, it covers interpretation, expression, and comparison of numbers in scientific notation, alongside all four basic arithmetic operations ...

22. Simplify Math with These Best 10 Scientific Notation Worksheets

This interactive worksheet from Live Worksheets can be completed as a whole-class activity using a smart board, or students can take part individually on their electronic devices. The worksheet contains 16 questions requiring conversion either from standard to scientific notation or the reverse. Suitable for Grade 8 upward.

23. Adding & subtracting in scientific notation

Express your answer in scientific notation. 8.2 ⋅ 10 − 5 + 0.0004 =. Stuck? Review related articles/videos or use a hint. Report a problem. Do 4 problems. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of ...