#### RESULTS

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Scientific notation calculator is used to add, subtract, multiply, and divide scientific notations. It can be used to evaluate micro scientific notation, Nano scientific notation, Pico scientific notation, and trillion in scientific notation as well. Scientific notations are difficult to solve because of the complexity involved in it. This is where write in scientific notation calculator comes in handy.

In this post, we will discuss scientific notation definition, scientific notation rules, scientific notation problems such as how to add scientific notation, how to multiply scientific notation, how to divide scientific notation, how to use scientific notation calculator, and much more.

## How to use Scientific Notation Calculator?

Scientific notation calculator is commonly referred to as exponential notation calculator. Most of the scientific notation calculations, such as addition or multiplication, could be time-consuming and exhausting because you have to deal with the exponents. Our calculator is developed by considering all those factors for the sake of simplicity of the user. To use this calculator, follow the steps below:

- Enter the first number: Mantissa on the left side and exponent on the right side in the first input box.
- Select the mode of operation from the given list.
- Enter the second number: Mantissa on the left side and exponent on the right side in the second input box.
- Press the Calculate button to see the output.

It will instantly give you the results in scientific notation, E notation, and decimal.

## What is Scientific Notation?

Scientific notation is a means to express numbers in a way that makes it easier to write numbers that are too small or too big. It is widely used as an arithmetical operation in mathematics, electronics, and science. The number is written as a base in the scientific notation, *b*, and the value multiplied by 10 to raise the power as exponent called ** n**.

`\(b \times 10^n\)`

For example, the speed of light is usually expressed in scientific notation because the number is too big to write in standard notation.

Speed of light scientific notation = `\(3.0 \times 10^8 m/s\)`

Below is the scientific notation chart in which scientific notation is compared with the equivalent standard notation for your understanding.

Power | Scientific Notation | Value |

-3 | 1 x 10^{-3} | 0.001 |

-2 | 1 x 10^{-2} | 0.01 |

-1 | 1 x 10^{-1} | 0.1 |

1 | 1 x 10^{1} | 10 |

2 | 1 x 10^{2} | 100 |

3 | 1 x 10^{3} | 1000 |

4 | 1 x 10^{4} | 10,000 |

5 | 1 x 10^{5} | 1,00,000 |

6 | 1 x 10^{6} | 10,00,000 |

## Scientific Notation Rules

We have to remember a few rules when working with scientific notations. Followings are some rules that you should follow before converting scientific notation to standard or applying any arithmetic operation to scientific numbers.

- The decimal has to be a non-zero number and should lie between the first two non-zero numbers.
- The number before the multiplication mark is called the mantissa or significant.
- The total numbers of digits in the significant are known as significant figures. You can use our Sig Fig Calculator to calculate significant figures.
- The exponent value is based on whether the decimal place is shifted to the left or to the right.

If you are wondering how to do scientific notation, read in the next section where we will discuss several scientific notation operations with scientific notation examples.

## Scientific Notation Operations

Adding and subtracting scientific notation is easy as compared to multiplying and dividing scientific notation. Let’s understand all arithmetic operations of scientific notations by using examples.

Suppose we have two scientific notations:

`\(x_1= 3 \times 10^3\)`

`\(x_2 = 2 \times 10^3\)`

### Addintion

Adding scientific notations is simple. If the base power is the same, add the mantissa and write the base 10 with unchanged power.

`\(x_1 + x_2 = \times 10^3 + 2 \times 10^3 = 5 \times 10^3\)`

### Subtraction

To subtract scientific notations, subtract the mantissa and write the base 10 with unchanged power.

`\(x^1 - x^2 = 3 \times 10^3 - 2 \times 10^3 = 1 \times 10^3\)`

### Multiplication

Multiplying scientific notations are different from adding or subtracting. In multiplication, the power of the base 10 is added, which is not the case in addition or subtraction.

`\(x_1 \times x_2 = (3 \times 10^3) \times (2 \times 10^3) = 1 \times 10^6\)`

### Division

Similar to multiplication, dividing scientific notations requires an operation on the powers of base 10. In division, powers of base 10 are subtracted to get the result.

`\(\dfrac{x_1}{x_2} = \dfrac{(3 \times 10^3)}{(2 \times 10^3)} = 1.5 \times 10^0 = 1.5\)`