# Scientific Notation Calculator

Created by Daniel Trojanowski and Wojciech Sas, PhD
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Jun 05, 2023

The scientific notation calculator will take any decimal value and convert it to scientific notation. Here we will not only tell you what scientific notation is all about but also explain the scientific notation rules and discuss slight variations that might appear in different domains where people use 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 a number a between 1 (included) and 10 (excluded) 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.

To better understand these rules of scientific notation, let's discuss an example.

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

Suppose we want to convert 0.00345 to scientific notation:

1. Place the decimal between the first two non-zero numbers, so we have 3.45.
2. Count the number of decimal places that were 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 in terms of a × 10ⁿ, in this case, 3.45 × 10⁻³.

Verify this result with our 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 accomplish this task. Also helpful in converting numbers to scientific notation is the exponent calculator.

## How to use the scientific notation converter?

It's very easy to use Omni's scientific notation calculator: just input a number and our converter will do the rest.

Note that this scientific notation converter 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.

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.

## FAQ

### How do I multiply and divide in scientific notation?

Suppose you have two numbers written in scientific notation: a × 10ⁿ and b × 10ᵐ.

• To multiply them, multiply the coefficients and add the exponents: (a×b) × 10ⁿ⁺ᵐ.
• To divide the first one by the second, divide the coefficients and subtract the exponents: (a/b) × 10ⁿ⁻ᵐ.
• The result need not be in scientific notation! It's recommended you verify if it is and perform the conversion if needed. You may use Omni's scientific notation calculator to do this task quickly and easily.

### What is 4,500 in scientific notation?

4.5×10³ or, equivalently, 4.5e3. This is because we want to write 4,500 as a × 10ⁿ with a ∈ [1,10) and n an integer.

### What is 0.00057 in scientific notation?

5.7×10⁻⁴ or, equivalently, 5.7e-4. In this way, we've written our number as a × 10ⁿ with a ∈ [1,10) and n an integer.

Daniel Trojanowski and Wojciech Sas, PhD
Enter either decimal or scientific notation
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