Decimal to Engineering Notation Calculator

Understanding Decimal to Engineering Notation Conversion

What is Engineering Notation?

Engineering notation is a form of scientific notation where the exponent of ten must be divisible by three. It's widely used in engineering and electronics to represent very large or very small numbers in a more readable format.

Formula for Engineering Notation

The general form of engineering notation is:

\[a \times 10^n\]

Where:

• \(a\) is a number greater than or equal to 1 and less than 1000
• \(n\) is an integer multiple of 3 (positive, negative, or zero)

Converting Decimal to Engineering Notation

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

1. Move the decimal point to the nearest multiple of three places from its original position.
2. Write down the number with the new decimal point position.
3. Count the number of places the decimal point was moved.
4. Write the number in the form \(a \times 10^n\), where \(a\) is the number with the new decimal point position, and \(n\) is the number of places the decimal point was moved (which will be a multiple of 3).

Calculation Steps

Let's convert 123456.789 to engineering notation:

1. Move the decimal point 5 places to the left (to the nearest multiple of 3):

   \[123.456789 \times 10^3\]

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

   \[123.46 \times 10^3\]

Example with Visual Representation

Let's visualize 123456.789 in engineering notation:

This diagram shows 123456.789 expressed in engineering notation as 123.46 × 10^3.