Scientific Notation Converter

Convert number to scientific notation, e-notation, and engineering notation or mentioned scientific notations to a number instantly, in real time with our easy to use tool.

Enter a number and see it change into other notations, you can also input numbers in other fields to see them change

Scientific notation is a crucial tool in mathematics and science, allowing us to express very large or very small numbers in a concise and manageable format. Let's learn the concept of scientific notation, demonstrate how to convert numbers to this format, and introduce related notations such as e-notation and engineering notation.

What is a scientific notation?

Scientific notation is a standardized way to write numbers that are too large or too small to be conveniently written in decimal form. It is particularly useful in scientific and mathematical contexts where we often deal with extreme values.

In scientific notation, a number is expressed as a product of two parts:

1. A coefficient (or mantissa) between 1 and 10

2. A power of 10 that indicates the scale of the number

The general form would be

a \times 10^n

Where 'a' is the coefficient (1 ≤ a < 10) and 'n' is an integer exponent.

How to convert a number to scientific notation?

Let us take 42,000 as an example.

To convert the number to scientific notation,

1. Shift the decimal point to the left until you have a number between 1 and 10. In our case, we move it 4 places: 4.2000

2. Count the number of places you moved the decimal point. The number of places you moved the decimal point becomes the exponent. We moved it 4 times, so our exponent is 4.

3. Write the number as the coefficient multiplied by 10 raised to the power of the exponent: 4.2 × 10^4

So, 42,000 in scientific notation is 4.2 × 10^4

What is e-notation?

E-notation is a variation of scientific notation commonly used in computer programming and digital displays. It replaces "× 10^" with the letter "E" or "e".

For example, 4.2 × 10^4 can be written as 4.2E4 or 4.2e4.

This notation is particularly useful in contexts where the multiplication symbol and superscript are not easily typed or displayed.

What is engineering notation?

Engineering notation is a specialized form of scientific notation used primarily in engineering and electronics. It differs from standard scientific notation in two key ways:

1. The exponent is always a multiple of 3 (e.g., 10^3, 10^6, 10^9)

2. The coefficient is always between 1 and 999.9

For example, the number 42,000 can be expressed in engineering notation as 42 × 10^3.

Converting Scientific Notation to a Number

Converting a number in scientific notation back to standard form is straightforward. Simply multiply the coefficient by 10 raised to the power of the exponent.

For example, to convert 4.2 × 10^4 back to standard form:

4.2 × 10^4 = 4.2 × 10,000 = 42,000

Similarly, 4.2E4 or 4.2e4 can be converted back to 42,000.

Comparing Scientific Notations

Scientific notation, e-notation, and engineering notation are all ways to express numbers in a concise and standardized format. While they differ slightly in presentation, they all serve the same purpose of representing very large or very small numbers in a manageable way. Here is a comparision table of the three mentioned notations.