# Scientific Notation ( Free Worksheets, Solved Examples and More)

**Scientific notation is a standard form of writing very small and very big numbers so that they can easily be used for computations and other calculations. A number in scientific notation is of the form a × 10^{n}, where a is a number between 1 and 9, inclusive and n can be a positive or a negative integer.**

For example: 300 is written as 3 × 10^{2} in scientific notation.Let us now learn more about scientific notation and the steps for adding, subtracting, multiplying, and dividing scientific notation.

Do you already know how to solve scientific notations? Get straight to the free scientific notation worksheets!

## Scientific Notation Worksheets – Addition, Subtraction, Division and Multiplication

Before we move on to the scientific notation worksheets, let us understand the concept a bit more. In a scientific notation, the decimal point of a number is moved till we get a number from 1 to 9 and value of *n* is the number of places the decimal is moved.

The exponent will be positive if we move the decimal point toward the left. If we move the decimal point towards the right, the exponent will be negative.

See the examples below:

*Example*: Write 8,380,000 in scientific notation.

8,380,000 is a whole number so decimal point will be at the end of the number, so here *a* = 8.38

Now *n* is the number of places the decimal is moved. Here we moved the decimal point towards the left, so exponent will be positive. So, *n* = 6.

So, 8,380,000 in scientific notation is written as **8.38 ****×**** 10 ^{6}**

*Example*: Write 0.00061 in scientific notation.

Here we move the decimal to the right so that we get a number from 1 to 9. So, *a* = 6.1

*n* is the number of places the decimal is moved. Here we moved the decimal point towards the right, so exponent will be negative. So, *n* = -4.

So, 0.00061 in scientific notation is written as **6.1** **×**** 10 ^{-4}**

### Adding and Subtracting Scientific Notation Worksheets with Solved Examples

We know how to write numbers in scientific notation, which means numbers have the same base that is 10. Next, let us go through the steps to be followed for adding or subtracting:

** Step 1:** Make the exponents equal to each other for which we should make the smaller exponent equal to the larger one by dividing with appropriate power of 10.

** Step 2:** Add or subtract the new coefficients.

** Step 3:** Write the answer in scientific notation, if it is not in scientific notation after adding or subtracting.

*Example*: Subtract 5.66 × 10^{1} – 3 × 10^{-2}

Here -2 is the smaller exponent, so multiply 3 × 10^{-2} by 10^{3} to make it 10^{1 }and divide by 10^{3},

So, 3 × 10^{-2} = = = = =

Now 5.66 × 10^{1} – 3 × 10^{-2} = 5.66 × 10^{1} – 0.003 × 10^{1} = (5.66 – 0.003) × 10^{1} = **5.657 ****×**** 10 ^{1}**

### Multiplying and Dividing Scientific Notation Worksheets and Solved Examples

To multiply or divide the numbers in scientific notation, we multiply or divide their coefficients and add their exponents. If after adding or subtracting the coefficients, the answer is not in scientific notation, then convert it to scientific notation.

** Step 1:** Multiply or divide the coefficients.

** Step 2:** Add or subtract the exponents.

** Step 3:** Convert the answer in scientific notation.

*Example*: Multiply (3.1 × 10^{-1})(0.4 × 10^{2})

** Step 1:** Multiply 3.1 and 0.4 that is 3.1 × 0.4 = 1.24

** Step 2:** Add the exponents, 10

^{-1}× 10

^{2}= 10

^{-1+2}= 10

^{1}

** Step 3:** (3.1 × 10

^{-1})(0.4 × 10

^{2}) = 1.24 × 10

^{1}

^{}

### CHECK POINT

Simplify and write each of the following in scientific notation.

- 0.000251
- 0.792 × 10
^{5} - (6.3 × 10
^{-2})(6.2 × 10^{2}) - (5.4 × 10
^{-1}) ÷ (2.7 × 10^{1}) - (3 × 10
^{-2})(9 × 10^{4}) - (3.6 × 10
^{3}) ÷ (0.6 × 10^{3})

##### Answer key

- 2.51 × 10
^{-4} - 7.92 × 10
^{4} - 3.906 × 10
^{1} - 2 × 10
^{-2} - 2.7 × 10
^{3} - 6

## eTutorWorld Understands Math Tutoring | Online Math Worksheets are Important Tools

Understanding graphs, charts, and opinion polls in a newspaper, for calculating house and car payments, and for choosing a long-distance telephone service are impossible without strong math skills …and the only way to develop strong math skills is by constant practice.

‘Practice makes a man perfect’ holds true for no other field better than for math. A middle or high school student must set aside a minimum of an hour for math every day. Other than textbooks, worksheets help you revise and understand concepts better.

Our expert tutors prepare online maths worksheets that are age and grade-appropriate. Grade-wise math worksheets for Elementary Math, Arithmetic, Pre-Algebra, Algebra, Geometry, Trigonometry, Statistics, Pre-Calculus and Calculus can be solved to improve math skills, to get ahead or to even catch up.

You may download these FREE online math worksheets in the PDF format, and then print and email us their solutions for a free evaluation and analysis by eTutorworld’smath expert tutors.

You may solve these worksheets by yourself or with your peers while studying together.

The Answer Key at the end of each worksheet allows for a self-evaluation.

## Personalized Online Tutoring

eTutorWorld offers affordable one-on-one live tutoring over the web for Grades K-12, Test Prep help for Standardized tests like SCAT, CogAT, MAP, SSAT, SAT, ACT, ISEE and AP. You may schedule online tutoring lessons at your personal scheduled times, all with a Money-Back Guarantee. The first one-on-one online tutoring lesson is always FREE, no purchase obligation, no credit card required.

For answers/solutions to any question or to learn concepts, take a **FREE CLASS.**

*No credit card required, no obligation to purchase. **Just book a free class to meet a tutor and get help on any topic you want!*

### FAQs

##### What is a scientific notation?

Scientific notation is a method used to represent very large or very small numbers in a more compact and readable form. It is written in the form of a number between 1 and 10 multiplied by a power of 10.

##### How to convert a number to scientific notation?

To convert a number to scientific notation, move the decimal point to the left or right so that there is one non-zero digit to the left of the decimal point. Count the number of places you moved the decimal point and add that as an exponent to 10.

##### How do you add and subtract numbers in scientific notation?

To add or subtract numbers in scientific notation, the exponents must be the same. If they are not, one number must be converted so that the exponents are the same. Once the exponents are the same, the numbers can be added or subtracted.

##### How do you multiply and divide numbers in scientific notation?

To multiply numbers in scientific notation, multiply the numbers and add the exponents. To divide numbers in scientific notation, divide the numbers and subtract the exponents.

##### What are some common uses of scientific notation?

Scientific notation is commonly used in scientific fields such as astronomy, physics, and chemistry to represent very large or very small numbers. It is also used in engineering and finance.

## Pricing for Online Tutoring

Tutoring Package | Validity | Grade (1-12), College |
---|---|---|

5 sessions | 1 Month | $139 |

1 session | 1 Month | $28 |

10 sessions | 3 months | $269 |

15 sessions | 3 months | $399 |

20 sessions | 4 months | $499 |

50 sessions | 6 months | $1189 |

100 sessions | 12 months | $2249 |

__Arithemetic & Pre Algebra__

**The Number System**

1) Rational and Irrational Numbers

2) Compare Irrational Numbers

3) Fractions and Repeating Decimals

4) Approximating Square Roots

__Algebra__

**Expressions and Equations**

1) Exponents and their properties

2) Square roots and Cube roots

3) Scientific Notation – addition, subtraction, division and multiplication

4) Equations with variables on both sides

5) Linear equations with one, zero, or infinite solutions

6) Age Word Problems

7) Solve systems of linear equations with elimination and substitution

8) Word Problems on System of Linear Equations

__Geometry__

1) Parallel Lines

2) Congruent Angles

3) Finding Angle Measures

4) Pythagorean Theorem

5) Distance Formula

6) Word problems on Volume of Cones, Cylinders, and Spheres

__Statistics and Probability__

## IN THE NEWS

Our mission is to provide high quality online tutoring services, using state of the art Internet technology, to school students worldwide.

**Online test prep and practice**

SCAT

SSAT

ISEE

PSAT

SAT

ACT

AP Exam

**Science Tutoring**

Physics Tutoring

Chemistry Tutoring

Biology Tutoring

**Math Tutoring**

Pre-Algebra Tutoring

Algebra Tutoring

Pre Calculus Tutoring

Calculus Tutoring

Geometry Tutoring

Trigonometry Tutoring

Statistics Tutoring

**Quick links**

Free Worksheets

Fact sheet

Sales Partner Opportunities

Parents

Passive Fundraising

Virtual Fundraising

Our Expert Tutors

Safe and Secure Tutoring

Interactive Online Tutoring

After School Tutoring

Elementary School Tutoring

Middle School Tutoring

High School Tutoring

Home Work Help

Math Tutors New York City

Press

©2022 eTutorWorld Terms of use Privacy Policy Site by Little Red Bird

©2022 eTutorWorld

Terms of use

Privacy Policy

Site by Little Red Bird