Scientific Notation Calculator

How to Convert Numbers to Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is widely used in scientific and engineering fields to simplify calculations and represent very large or very small quantities.

Formula

The general formula for scientific notation is:

\[ a \times 10^n \]

Where:

• a is the coefficient (1 ≤ |a| < 10)
• n is the exponent (an integer)

Calculation Steps

1. Move the decimal point in the number until you have a number between 1 and 10 (not including 10).
2. Count how many places you moved the decimal point. This will be your exponent.
3. If you moved the decimal point to the left, the exponent is positive. If you moved it to the right, the exponent is negative.
4. Write the number in the form a × 10^n, where a is the number between 1 and 10, and n is the exponent you found.

Example

Let's convert 45,000 to scientific notation:

1. Move the decimal point 4 places to the left: 4.5000
2. The coefficient (a) is 4.5
3. We moved the decimal 4 places to the left, so the exponent (n) is 4
4. Therefore, 45,000 in scientific notation is 4.5 × 10^4

Visual Representation

This diagram illustrates how 45,000 is converted to 4.5 × 10^4 in scientific notation.