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# Scientific Notation Calculator

By Daniel Trojanowski and Wojciech Sas, PhD candidate

The scientific notation calculator will take any decimal value and convert it to scientific notation.

## What is Scientific Notation?

Scientific notation is generally used with very large or very small numbers in applications such as physics, engineering and chemistry. It condenses the numbers into the form into a number multiplied by `10` raised to an exponent, denoted as `a * 10ⁿ`.

## Scientific Notation Rules

When converting a number into scientific notation, we must remember a few rules. First, the decimal must be between the first two non-zero numbers. The number prior to the multiplication symbol is known as the significant or mantissa. The numbers of digits in the significant depends on the application and are known as significant figures. The significant figures calculator can assist in this situation. The value of the exponent depends on whether or not the decimal place is moved to the right or left to return to the original number. An example on how to convert a number into scientific notation is done in the next section.

## How to Use the Scientific Notation Converter

Suppose we want to convert `0.00345` to scientific notation. Use the following steps:

1. Place the decimal between the first two non-zero numbers, so we have `3.45`.
2. Count the number of decimal places that was moved, which in this case is `3`.
3. Determine whether the decimal point must be moved to the left or right to return to the original number.
4. If the decimal is moved right, the exponent is negative. If the decimal is moved left, the exponent is positive.
5. Write is terms of `a * 10ⁿ`, in this case `3.45 * 10⁻³`
6. Check your results with the scientific notation calculator.

If you wanted the answer to have two significant figures, you would have to round the significant to `3.5`. The rounding calculator is a great tool to use to accomplish this task. Also useful in converting numbers to scientific notation is the exponent calculator.

If you are searching for useful maths calculators do not hesitate to take a look at the cube root calculator which enables you to calculate not only cube root but also roots of any degree.

Note that the scientific notation calculator uses e plus or minus the exponent, instead of 10 raised to the exponent. There are several different notations used, depending on the application. Computer languages, engineering and mathematical applications use similar but different ways to represent scientific notation.

Daniel Trojanowski and Wojciech Sas, PhD candidate