**Math Calculators** ▶ Scientific Notation Calculator

An online scientific notation calculator allows you to add, subtract, multiply, and divide numbers in scientific notation. Also, this online scientific notation converter helps you to convert a number to scientific notation, e notation, engineering notation and decimal notation. Just give a read to this post to know how to do scientific notation conversions with a calculator or manually (step-by-step), examples of scientific notation calculations, and much more! But, before knowing these all legitimate terms, let’s begin with the basic definition of scientific notation.

Scientific notation is commonly used with all those numbers that are very large or even very small. It is mostly used in many fields that are related to science such as calculations of physics, applications of engineering and formulas of chemistry. It basically shrinks all the numbers into a specific form that is multiplied by 10 and then raised to an exponent. In every field of science, it is represented by * 10ⁿ. N is the power and 10 is the exponent.

**Scientific Notation – Scientific Notation Chart**

10^{9} = |
1,000,000,000 | Giga (G) |

10^{8} = |
100,000,000 | |

10^{7} = |
10,000,000 | |

10^{6} = |
1,000,000 | Mega (M) |

10^{5} = |
100,000 | |

10^{4} = |
10,000 | |

10^{3} = |
1,000 | Kilo (K) |

10^{2} = |
100 | |

10^{1} = |
10 | |

10^{0} = |
1 | |

10^{-1} = |
0.1 | |

10^{-2} = |
centi (c) | 0.01 |

10^{-3} = |
milli (m) | 0.001 |

10^{-4} = |
0.0001 | |

10^{-5} = |
0.00001 | |

10^{-6} = |
micro (µ) | 0.000001 |

10^{-7} = |
0.0000001 | |

10^{-8} = |
0.00000001 | |

10^{-9} = |
nano (n) | 0.000000001 |

Whenever you are converting any number into scientific notation format, you need to remember a few set of rules to make the conversion accurately. Basic rules are clarified below:

- First of all, you must have to keep in mind that the decimal should be present between the first two numbers that are non-zero.
- All those numbers that are prior to the multiplication symbol are usually acknowledged as significant or mantissa.
- All the numbers of digits that are significant always depend on the application or field in which they are being used and they are known as significant figures.
- In the significant figures, the value of the exponent always depends on whether or not the decimal place or point is relocated to the right side or to the left side to return to the original number.

Have a look at the following example to have a clear concept of scientific notation:

Example:

If you have a number 700 then how to write in scientific notation?

In the first step to convert form number to scientific notation we will separate the ten and hundred: 700 (whole number) = 7 (ten) × 100 (hundred)

In the second step we will convert 100 into exponent and raised power: 100 = 10 raised to power 2

Therefore 700 will be = 7 × 10 raised to power 2

In this way Both numbers 700 and 7 × 10 raised to power 2 have the exactly same values. They are just represented in different ways. However scientific notation conversion calculator is the best way to verify the calculations.

Some of the basic terms that are commonly involved in scientific notation are explained below:

Scientific E notation is the most basic and easy way to write all those numbers that are too large or too small. It is helpfully for all those numbers that cannot be written in the decimal formats. Exponential notation calculator is functioned to display numbers in terms of “times ten raised to the power of” without the hustle of manual calculation. However, a representation of manual calculation is elaborated below:

- The number that is “3.02E12” in E notation will be elaborated as = 3.02 * 1012. Further this number “3.02 * 1012” will be equals to 3,020,000,000,000
- The exponent that is involved in the E notation is normally represented by “bEn” or simply by “E”. In the term bEn the word b is the representation of base, E is the representation of “x 10” and then finally n is written after the E. there is a difference between the representation of scientific notation and E notation. The basic difference among their visual representation is elaborated below:
- 5 × 100 is the scientific notation whereas the same number in terms of E notation will be represented as 5E0.
- As e notation involves exponents therefore exponential notation calculator is the best option to deal with the calculations that involve e notation.

- Engineering notation has some similarities with the scientific notation but it also has some distinctive differences. In the engineering notation the exponent, n, is limited to multiples of 3 such as: 0, 3, 6, 9, 12, -3, -6, and so on.
- In this term all the numbers that are align with SI prefixes and you can be read as such. It is important to keep in mind that all the decimal place of any number can be conveniently moved to write the scientific notation in engineering notation. However, while using scientific notation conversion calculator this problem will be solved automaticlly as it writes in Engineering notation by following rules without any specific commands.

Any number can be converted to engineering notation by following certain rules:

- First of all, you have to move the decimal point from the end of the given number to the left side altogether in the form of groups of 3 places until you get at least 1.
- There should be no more than 3 digits to the left place of the decimal point. However, a scientific converter is the best option to convert a number to engineering notation.

**Example:**

If the number is in the scientific notation such as: 1.234 × 10 raised to power 8then how will it be converted in Engineering notation?

- In the engineering notation it will be represented as: 123.4 × 10 raised to power 6.

It is the representation of any fraction as well as of any real number that uses the base of ten and it can be consist of any of the digits like 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, along with a decimal point. To convert form scientific notation to decimal notation there all you have to do is to move the decimal place and then write it in the form of power of 10. However, a decimal notation calculator is the best way for this conversion.

**Example:**

**How to convert scientific notation 1.5 × 102 to decimal format?**

For this purpose, just follow two simple steps below:

- 1.5 × 10 raised to power 2 = 1.5 × 100
- 1.5 × 10 raised to power 2 = 150
- For the conversion of decimal to scientific notation you have to create the initial equation and then move the decimal point.

From Scientific notation to decimal might be seen as a tricky process but a number or a fraction can be converted into decimal notation with ease. For example, if the fraction is 3/2 then you can divide number 3 by number 2 to get converted into decimal notation. It will be equal to 1.5.

In the form of scientific notation, the procedures of addition, subtraction, multiplication, and division is slightly different. Scientific notation calculator can perform all these functions with accuracy. Below are some manual examples of these methods.

For addition and for subtraction all the numbers will be converted to the same power of 10, and after this step digit terms will be added and subtracted.

- Example of addition: (4.215 x 10-2) added in (3.2 x 10-4) = (4.215 x 10-2) added in (0.032 x 10-2) = 4.247 x 10-2
- Example of subtraction: (8.97 x 104) subtracted from (2.62 x 103) = (8.97 x 104) subtracted from (0.262 x 104) = 8.71 x 104

- For the multiplication of the scientific notation terms you have to follow all the steps of normal multiplication.
- All the digit terms will be multiplied in the most normal way and after that all the present exponents will be added.
- The end result will be changed so that there will be only one nonzero digit to the left side of the decimal.

Example: (3.4 x 106) multiplied by (4.2 x 103) = (3.4) (4.2) multiplied by 10(6+3) = 14.28 x 109 = 1.4 multiplied by 1010

- In the process of division of all the scientific notation terms, all the digit terms will be divided in the normal way and after that, all the exponents will be subtracted.
- The quotient can be changed if there is a need to change it so that there will be only one nonzero digit to the left side of the decimal place.

Example: (6.4 x 106) divided by (8.9 x 102) = (6.4) divided by (8.9) multiplied by 10(6-2) = 0.719 x 104 = 7.2 multiplied by 103

Thankfully, you come to know about the operations with Numbers written in scientific notation.

An online scientific notation calculator by calculator-online helps you in adding, subtracting, multiplying, and dividing numbers in scientific notation. Also, our free scientific notation converter helps you to convert a number to:

- Scientific Notation
- E Notation
- Engineering Notation
- Decimal Notation

A scientific notation calculator is 100% free and you can easily convert any number into standard notations by using these given step by step parameters:

**Inputs:**

- Hit the “Scientific Notation Calculator” tab
- Then, you have to enter the first number into the designated box with the power of 10
- Now, you have to choose the operation from the drop-down menu according to which you want to perform standard notation calculations, it can either be (+), (-), (*), (/)
- Very next, you have to enter the second number into the given field, it also entered as a power of 10
- Now, just hit the calculate button to get quick result

**Outputs:**

The scientific notation conversion calculator will generate the results after applying selected operation on the given inputs; you will get results in the following formats:

- Scientific Notation
- E Notation
- Engineering Notation
- Decimal Notation

**Inputs:**

- Hit the “Scientific Notation Converter” tab

There are three given fields:

- Scientific Notation
- Decimal Notation
- E Notation
- You just have to enter value in one of the above fields to get the conversions in other notations
- Once you entered the value, hit the calculate button

**Outputs:**

The converter shows the results in the following formats:

- Scientific Notation
- E Notation
- Engineering Notation
- Decimal Notation

If you have numbers in billions, then you can convert them in scientific notation for the ease of calculations.

- The exact and precise format for the scientific notation in the scientific notation calculator and in the manual calculations is a x 10^b.
- In this representation a is a number. It might be a decimal number such that the absolute value of a can be greater than or equal to one and also less than ten or, 1 ≤ |a| < 10.
- In the above representation of scientific notation, the term b is the power of 10 that is required so that the scientific notation can mathematically equivalent to the original or real number.
- When you are converting scientific notation to a number you have to move the existing decimal point of your number until there is only one non-zero digit to the left side of the decimal point. The resulting decimal number will be a.
- Now simply count how many places you have moved the decimal point. This number will be b. If you have moved the decimal place to the left side, then the resulting number b will be positive. On the other hand, if you have moved the decimal place to the right side then the resulting number b will be negative.
- If there is no need to move the decimal place, then the resulting number b will be equal to zero.
- You can write your scientific notation number as a x 10^b and you can read it as “a time 10 to the power of b.”
- Trailing 0 will be removed only if it exists to the left side of the decimal place.

**Example: Convert a number “357,096” to a Scientific Notation format.**

- First of all, you have to Move the decimal 5 places to the left side so that you can get a number“3.57096”
- to 5 Now you have a that is equal to “3.57096”
- In the above example, you have moved the decimal place to the left side so b will be positive
- Therefore, the resulting number b will be equal
- Therefore, now you can convert the number 357, to 3.57096 x 10^5 as scientific notation.

You can Convert any Scientific Notation to a Real Number manually as well as with the support of the scientific notation converter.

- First of all, you have to multiply the decimal number by 10 raised to the power that is indicated.
- For example, if the scientific notation is “3.456 x 10^4” then while converting it into number it will be equal to 3.456 x 10,000. After simplification, we will get = 34560.
- On further calculation we will get 3.456 multiplied by 10^-4 = 3.456 multiplied by .0001 = 0.0003456

Follow the given steps to use scientific notation on a scientific calculator:

- First of all, you have to enter the number M on the calculator
- Very next, you have to hit the multiplication button
- Now, you have to enter the number 10
- Then, there’s need to hit the exponent button, this is the button that varies on different calculators, but it will be something like xy, ay, exp, or ^
- Now, you have to enter the number N on the calculator
- Just hit the “enter” button

You just have to simply account the above calculator for scientific notation or take a look at the above-mentioned example for better understanding.

One million (1,000,000) in scientific notation written as 1 x 10^6.

When a number between 1 and 10 is multiplied by a power of 10, this number is said to be written in scientific notation. For instance, 750,000,000 can be written in scientific notation as 7.5 ✕ 10^8.

17210000000 written in scientific notation as 1.721 x 10^ 10.

31 billion in scientific notation written as 3.100 x 10^ 10.

52 thousandths or 0.052 in scientific notation written as 5.200 x 10^ -2.

Let’s take a look at the example:

- 5.703 x 10^7
- 5.703 with 10 power 7 means:
- 5.7030000
- So, 57,030,000

54 in scientific notation is written as 5.400 x 10^ 1.

13040000 in scientific notation is written as 1.304 x 10^7.

53,010,000 in scientific notation is written as 5.301 x 10^7.

0.0970 in scientific notation is written as 9.700 x 10^ -2.

0.00019 (nineteen hundred thousandths) in scientific notation is written as 1.900 x 10^ -4.

0.02 in scientific notation is written as 2 x 10-2.

9 ten thousandths is equal to 0.0009 which is written in scientific notation as 9 x 10^-4.

This scientific notation conversion calculator is one of the finest ways to provide support in all those complex mathematical calculations that involve E notation, engineering notation, scientific notation, and decimal notation in no time. This scientific notation converter has the ability to convert from one format to another in the blink of an eye. it provides help in the learning process of different notations and the best available option for students and professionals for learning purposes. To assess the accuracy of your answers this tool is the most convenient choice.

From the source of Wikipedia: Scientific notation, Normalized notation, Engineering Notation, Significant figures, and much more!

From the source of brilliant: Scientific notation format is standardized to be easy to read, explore more about it.

From the authorized source of study: Scientific notation rules and examples.

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