Decimal to Scientific Notation Calculator

Scientific Notation Visualization
Original Number Invalid Scientific Notation Invalid

Understanding Decimal to Scientific Notation Conversion

What is 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 science, engineering, and mathematics.

Formula for Scientific Notation

The general form of scientific notation is:

a×10n

Where:

  • a is a number greater than or equal to 1 and less than 10
  • n is an integer (positive, negative, or zero)

Converting Decimal to Scientific Notation

To convert a decimal to scientific notation, follow these steps:

  1. Move the decimal point to the right of the first non-zero digit.
  2. Count the number of places the decimal point was moved.
  3. Write the number in the form a×10n, where a is the number with the decimal point after the first digit, and n is the number of places the decimal point was moved.

Calculation Steps

Let's convert 123456.789 to scientific notation:

  1. Move the decimal point 5 places to the left:

    1.23456789 × 10^5

  2. Round to the desired number of decimal places (let's say 2):

    1.23 × 10^5

Example with Visual Representation

Let's visualize 123456.789 in scientific notation:

123456.789 Move decimal 1.23456789 × 10^5 1.23 × 10^5 Move decimal 5 places left Round to 2 decimal places Final scientific notation: 1.23 × 10^5

This diagram shows 123456.789 expressed in scientific notation as 1.23 × 10^5.