scientific notation problem solving worksheet

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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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• Scientific Notation
• Operations with Scientific Notation

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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.

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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)

POPULAR TAGS   :    Scientific notation worksheet pdf,  Operations with scientific notation worksheet,  Adding and subtracting scientific notation worksheet,  Scientific notation word problems worksheet,  Scientific notation to standard form worksheet

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How to Solve Scientific Notation? (+FREE Worksheet!)

Learn how to solve mathematics problems containing scientific notation in a few simple and easy steps.

Related Topics

• How to Solve Powers of Products and Quotients
• How to Multiply Exponents
• How to Divide Exponents
• How to Solve Zero and Negative Exponents
• How to Solve Negative Exponents and Negative Bases

Step by step guide to solve scientific notation problems

• Scientific notation is used to write very big or very small numbers in decimal form.
• In scientific notation all numbers are written in the form of: \(m×10^n\)

Scientific Notation – Example 1:

Write \(0.00015\) in scientific notation.

First, move the decimal point to the right so that you have a number that is between \(1\) and \(10\). Then: \(N=1.5\) Second, determine how many places the decimal moved in step \(1\) by the power of \(10\). Then: \(10^{ \ -4} →\) When the decimal is moved to the right, the exponent is negative. Then: \(0.00015=1.5×10^{ \ -4} \)

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Scientific notation – example 2:.

Write \(9.5 \times 10^{\ -5}\) in standard notation.

\(10^{-5} →\) When the decimal is moved to the right, the exponent is negative. Then: \(9.5×10^{-5}=0.000095\)

Scientific Notation – Example 3:

Write \(0.00012\) in scientific notation.

First, move the decimal point to the right so that you have a number that is between \(1\) and \(10\). Then: \(N=1.2\) Second, determine how many places the decimal moved in step \(1\) by the power of \(10\). Then: \(10^{-4}→ \) When the decimal is moved to the right, the exponent is negative. Then: \(0.00012=1.2×10^{-4}\)

Scientific Notation – Example 4:

Write \(8.3×10^{-5}\) in standard notation.

\(10^{-5} →\) When the decimal is moved to the right, the exponent is negative. Then: \(8.3×10^{-5}=0.000083\)

Exercises for Solving Scientific Notation

Write each number in scientific notation..

• \(\color{blue}{91 × 10^3}\)
• \(\color{blue}{60}\)
• \(\color{blue}{2000000}\)
• \(\color{blue}{0.0000006}\)
• \(\color{blue}{354000}\)
• \(\color{blue}{0.000325}\)

Download Scientific Notation Worksheet

• \(\color{blue}{9.1 × 10^4}\)
• \(\color{blue}{6 × 10^1}\)
• \(\color{blue}{2 × 10^6}\)
• \(\color{blue}{6 × 10^{–7}}\)
• \(\color{blue}{3.54 × 10^5}\)
• \(\color{blue}{3.25 × 10^{–4}}\)

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by: Effortless Math Team about 4 years ago (category: Articles , Free Math Worksheets )

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SCIENTIFIC NOTATION WORD PROBLEMS WORKSHEET

Problem 1 :

The table below shows the population of the three largest countries in  North America in 2011. Find the total population of these countries.

Problem 2 :

When the Sun makes an orbit around the center of the Milky Way, it travels  2.025 x 10 14   kilometers. The orbit takes 225 million years. At what rate  does the Sun travel? Write your answer in scientific notation.

Problem 3 :

Light travels at a speed of 1.86 x 10 5  miles per second. It takes light from the Sun about 4.8 x 10 3  seconds to reach Saturn. Find the approximate distance from the Sun to Saturn. Write your answer in scientific notation.

Problem 4 :

Light travels at the speed of 1.17 x 10 7  miles per minute. Pluto’s average distance from the Sun is 3,670,000,000 miles. On average, how long does it take sunlight to reach Pluto? Write your answer in scientific notation.

Detailed Answer Key

Step 1 : 

First, write each population with the same power of 10.

United States : 3.1 x 10 8

Canada : 0.338 x  10 8

Mexico : 1.1 x  10 8

Step 2 : 

Add the multipliers for each population.

3.1 + 0.338 + 1.1  =  4.538

Step 3 : 

Write the final answer in scientific notation :

4.538 x  10 8

First, write each number in standard notation.

United States :  310,000,000

Canada :  33,800,000

Mexico :  110,000,000

Find the sum of the numbers in standard notation.

310,000,000 + 33,800,000 + 110,000,000  =  453,800,000

453,800,000  =   4.538 x  10 8

Key points : 

The answer is the number of kilometers per year that the Sun travels  around the Milky Way.

Set up a division problem using

Rate  =  Distance / Time 

to represent the situation.

Substitute the values from the problem into the Rate formula. 

Write the expression for rate with years in scientific notation.

That is, 225 million  =  2.25 x  10 8 .

Then, we have

Find the quotient by dividing the decimals and using the laws of exponents.

Divide the multipliers.

2.025 ÷  2.25  =  0.9 

Divide the powers of 10.

10 14  ÷  10 8   =   10 14-8  

10 14  ÷  10 8   =   10 6  

Combine the answers to write the rate in scientific notation.

0.9 x  10 6    =  9.0 x 10 5

Justify and Evaluate : 

Use estimation to check the reasonableness of your answer.

9.0 x 10 5  is close 10 6 ,  so the answer is reasonable.

As we have solved question 2, we can solve get answer for this question using the formula for distance given below. 

Distance  =  Speed x Time

Then, we will get the answer : 

8.928 x 10 8  miles

As we have solved question 2, we can solve get answer for this question using the formula for time given below. 

Time   =  Distance / Speed  

3.14 x 10 2 minutes

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Scientific Notation Word Problems Worksheets

What is Scientific Notation? How wonderful it is to find out that you can write short forms instead of going on writing long digit numbers. You should be thankful for the discovery of scientific notation concepts; you can save the effort of writing continuously long digits. To put it simply, scientific notation is writing the short forms of very long numbers. Instead of writing the number in decimal form, scientific notation helps in making the short. The number is multiplied by the power of ten and shortened. In mathematical notation, the first number is the 'coefficient.' It is always greater than or equal to one and less than 10. For instance, to write the scientific notation for 256, the coefficient has to be shortened to 2.56 However, the second number in the equation is expressed in the form of a power of 10, written as 10 with an exponent. Combining these two numbers, you will get a kind of equation like this. 2.56 x 10 2 . In case you see a negative exponent, it shows that the decimal has to be moved to the left.

Aligned Standard: Grade 8 Expressions and Equations - 8.EE.A.4

• Population Problem Step-by-Step Lesson - We do a little scientific notation subtraction to solve this one. Very basic at first.
• Guided Lesson - The mass of the Earth and the Sun get in the mix; along with another population problem.
• Guided Lesson Explanation - When answering these types of problems you will need plenty of space to spread out your answer.
• Independent Practice - These are such random questions. I did Google to find actual realistic numbers for them. Who really figured out how much a dust particle weighed?
• Matching Worksheet -Match the circumstances to their outcomes. You will find these problems a bit challenging to step up.
• Answer Keys - These are for all the unlocked materials above.

Homework Sheets

When students first see the length of problems like this they are intimidated.

• Homework 1 - In 2010, there were approximately 6 million girls living in Orange City. In 2011, the population was down to 4 million girls. How many girls lived in Orange City in 2011 in comparison to 2010? Write your answer in scientific notation.
• Homework 2 - Get them into the same power of ten to make it workable. A nice way to do that is to move the decimal one to the right on Lake City’s population. This results in losing a power of ten.
• Homework 3 - Suppose there are 3 × 10 6 fish in every 2 km area of sea. How many fish are there in 6 km of sea?

Practice Worksheets

Once students master the art of outlining, these problems become much easier for them.

• Practice 1 - 0.000078 is the wave length of white light. Can you express the measurement using scientific notation?
• Practice 2 - In India, the population was 500 million people in 2000. The total health care costs for the country at that time were $ 2.5 trillion. Calculate the average amount spent per person on health care.
• Practice 3 - wo men are working together on a project. The first man earns 3 x 10 5 dollars and the second one earns 3 x 10 4 dollars for the project. How much more money does the first man earn?

Math Skill Quizzes

Remind students that when the tail ends of scientific notation is the same, they cancel.

• Quiz 1 - A robbery in London resulted in 6,040,000,000 pounds being stolen. Write this number in scientific notation.
• Quiz 2 - If the population of Vatican City spends 40 million Euros in 40 days, find the amount spent in 15 days.
• Quiz 3 - Microwave ovens work at a wave frequency of 3 x 10 3 MHz. What will be the wave frequency if we use 1/3 of the frequency?

Example: Scientific Notation Word Problem

Problem: In 2019, the U.S. population was calculated to be 328.2 million people by the national Census Bureau. In that same year the healthcare cost of that nation were $3.8 trillion dollars. Determine the cost of healthcare per person in the nation at that time?

Solution: To determine this value we will need to divide the total cost ($3.8 trillion) by the number of people (328.2 million). But first we need to get these values into a workable format. This is where our powers of ten and scientific notation come in handy.

Step 1) Convert the Values to Scientific Notation

A million can be expressed as 10 6 . So, 328.2 million can be expressed as: 328.2 x 10 6 .

A trillion can be expressed as 10 12 . So, 3.8 trillion can be expressed as: 3.8 x 10 12 .

Step 2) Divide Cost by the Number of People

We just have to setup the math. We would place our values that are now in scientific notation into the original quotient that we were trying to determine. We can call this unknown cost per person the variable x. So, we would write it as:

We can remove those decimal values by dropping a power of ten for each decimal we remove. In this case there is only one decimal value in each. So, this can be rewritten as:

We can then rewrite this as a fraction multiplied by a combined power of ten, as you will see below:

Convert the fraction to a decimal and combine the powers of ten:

x = 0.0116 x 10 6

We state this value as dollar figure to answer our problem:

0.0116 x 10 6 = $11,600.

This means that the United States spent $11,600 per person on healthcare in 2019.

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Scientific Notation Worksheets 8th Grade

Scientific notation worksheets 8th grade  helps understand the 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.

Benefits of 8th Grade Scientific Notation Worksheets

The benefit of scientific notation worksheets 8th grade ensures visual simulations that help students experience the action and understand the concept clearly. Scientific notation worksheets for grade 8 not just help students mathematically but also help them deal with real-life problems thus boosting the problem-solving skills of the student. These 8th grade math worksheets come along with answer keys with detailed step-by-step solutions for all the practice questions that help students understand the concept better.

Printable PDFs for Grade 8 Scientific Notation Worksheets

Students can download the grade 8 scientific notation worksheets in a PDF format for free.

• Math 8th Grade Scientific Notation Worksheet
• 8th Grade Scientific Notation Math Worksheet
• Eighth Grade Scientific Notation Worksheet
• Grade 8 Math Scientific Notation Worksheet

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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 83 times this week and 346 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.

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Free Printable Scientific Notation Worksheets for 7th Grade

Scientific Notation Worksheets: Discover a collection of free printable resources for Grade 7 Math teachers to help students master the art of expressing numbers in scientific notation format.

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Explore printable Scientific Notation worksheets for 7th Grade

Scientific Notation worksheets for Grade 7 are an essential tool for teachers looking to enhance their students' understanding of math and number sense. These worksheets provide a variety of exercises and problems that challenge students to apply their knowledge of scientific notation in different contexts. By incorporating these worksheets into their lesson plans, teachers can ensure that their Grade 7 students develop a strong foundation in this critical area of mathematics. Furthermore, these worksheets can be easily adapted to suit the needs of individual learners, making them a versatile resource for educators. With a range of difficulty levels and topics covered, Scientific Notation worksheets for Grade 7 are a valuable addition to any math curriculum.

Quizizz is an excellent platform for teachers to access a wide range of resources, including Scientific Notation worksheets for Grade 7, as well as other math and number sense materials. This platform offers a variety of interactive quizzes, games, and activities that can be easily integrated into lesson plans to engage students and reinforce their learning. Teachers can also use Quizizz to track their students' progress and identify areas where additional support may be needed. By incorporating Quizizz into their teaching strategies, educators can create a dynamic and interactive learning environment that caters to the diverse needs of their Grade 7 students. With its extensive library of resources and user-friendly interface, Quizizz is an invaluable tool for teachers looking to enhance their students' understanding of math and number sense.