Scientific Notation: The Shortening of a Number

What is Scientific Notation?

Scientific notation is a way to represent a number (large or small)  that allows us to give a "shorthand way" of writing out a number. Imagine having to write out the number 938,000,000,000, ten times. It would not take you long before you realized that writing it this way is a lot of work. Scientific notation would allow us to represent the number 938,000,000,000 by saying it is equivalent to 9.38 X 10^11. This has obvious advantages when working with numbers all day long.

This method can be used with incredibly small numbers as well (the difference being the exponent in the notation). Instead of having a positive exponent, you would have a negative.

So how do we do it?

It's really quite simple. When representing a large number, move your decimal place over to the right of the first non-zero digit (in this case, 9). Counting the number of places you move the decimal, this will give you the exponent you will need to use. We used the exponent (11) because we moved the decimal 11 places to the left.

Let's go the opposite way:

Let the new number be the following: 0.00000682. Represent it using scientific notation.

6.82 X 10^-6. Since 6 is the first non-zero digit, we place the decimal to the right of that place value. This allows us to move the decimal 6 places to the right - meaning the exponent is negative.

The following is a YouTube video explaining scientific notation:

Scientific Notation