# Scientific Notation Calculator

A Scientific Notation Calculator is a convenient tool for performing calculations involving numbers expressed in scientific notation. It simplifies the process of multiplying, dividing, adding, and subtracting numbers with exponents quickly and accurately. With this calculator, you can input numbers in scientific notation format and perform calculations effortlessly.

## Scientific Notation Calculator

A Scientific Notation Calculator is a tool that allows you to perform calculations involving numbers written in scientific notation. It enables you to easily multiply, divide, add, and subtract numbers with exponents. This calculator simplifies the process of working with large or small numbers by converting them into scientific notation format and performing the desired operations accurately.

## Result

## Scientific notation calculations

For 2 number x1 and x2:

*x*_{1} = *a*_{1} × 10^{b1}

*x*_{2} = *a*_{2} × 10^{b2}

### Scientific notations addition

*x*_{1} +
*x*_{2}
= *a*_{1} × 10^{b1} + *a*_{2} × 10^{b2}

### Scientific notations subtraction

*x*_{1} - *x*_{2}
= *a*_{1} × 10^{b1} - *a*_{2} × 10^{b2}

### Scientific notations multiplication

*x*_{1} × *x*_{2}
= *a*_{1}*a*_{2} × 10^{b1+b2}

### Scientific notations division

*x*_{1} / *x*_{2}
= (*a*_{1}/*a*_{2}) × 10^{b1-b2}

### Scientific notation

Scientific notation is a way to express numbers in a form that makes numbers that are too small or too large more convenient to write. It is commonly used in mathematics, engineering, and science, as it can help simplify arithmetic operations. In scientific notation, numbers are written as a base, **b**, referred to as the significand, multiplied by 10 raised to an integer exponent, **n**, which is referred to as the order of magnitude:

b × 10^{n}

Below are some examples of numbers written in decimal notation compared to scientific notation:

Decimal notation | Scientific notation |

5 | 5 × 10^{0} |

700 | 7 × 10^{2} |

1,000,000 | 1 × 10^{6} |

0.0004212 | 4.212 × 10^{-4} |

-5,000,000,000 | -5 × 10^{9} |

### Engineering notation

Engineering notation is similar to scientific notation except that the exponent, **n**, is restricted to multiples of 3 such as: 0, 3, 6, 9, 12, -3, -6, etc. This is so that the numbers align with SI prefixes and can be read as such. For example, 10^{3} would have the kilo prefix, 10^{6} would have the mega prefix, and 10^{9} would have the giga prefix. Note that the decimal place of the number can be moved to convert scientific notation into engineering notation. For example:

1.234 × 10^{8} (scientific notation)

can be converted to:

123.4 × 10^{6} (engineering notation)

### E-notation

E-notation is almost the same as scientific notation except that the "× 10" in scientific notation is replaced with just "E." It is used in cases where the exponent cannot be conveniently displayed. It is written as:

bEn

where **b** is the base, **E** indicates "x 10" and the **n** is written after the **E**. Below is a comparison of scientific notation and E-notation:

Scientific notation | E-notation |

5 × 10^{0} | 5E0 |

7 × 10^{2} | 7E2 |

1 × 10^{6} | 1E6 |

4.212 × 10^{-4} | 4.212E-4 |

-5 × 10^{9} | -5E9 |

The "E" can also be written as "e" which is what is used by this calculator. It can also be written in other ways depending on the context, such as being represented differently in different programming languages.

### Scientific Notation Calculator Example

Number | Scientific Notation (Standard Form) |
---|---|

123456789 | 1.23456789 x 10^8 |

0.000012345 | 1.2345 x 10^-5 |

9876543210 | 9.87654321 x 10^9 |

0.00000000098765 | 9.8765 x 10^-13 |

30000000000 | 3.0 x 10^10 |

In this table, the "Number" column represents the input number, and the "Scientific Notation (Standard Form)" column shows the same number expressed in scientific notation.

For instance, the number 123,456,789 is written in scientific notation as 1.23456789 x 10^8. Similarly, the number 0.000012345 is represented as 1.2345 x 10^-5 in scientific notation.

The Scientific Notation Calculator simplifies large or small numbers by expressing them in a compact form using powers of ten. This notation is commonly used in scientific and mathematical calculations when dealing with very large or very small values. It allows for easier representation and comparison of numbers across different scales.