Exponents and Scientific Notation: Learn It 5

Scientific Notation

Scientific notation is a way of writing numbers that are very large or very small in a compact and convenient form. It is widely used in the sciences, engineering, and mathematics, and is especially useful for dealing with numbers that have a lot of zeros.

scientific notation

In scientific notation, a number is written as a product of two parts: a coefficient and a power of [latex]10[/latex].

 

It is written in the form [latex]a\times {10}^{n}[/latex], where [latex]1\le |a|<10[/latex] and [latex]n[/latex] is an integer.   [latex]n[/latex] can be positive or negative depending on whether a small or large number is being converted to scientific notation.

When converting large numbers, [latex]n[/latex] is positive. When converting small numbers, [latex]n[/latex] is negative.
Consider the number [latex]2,780,418[/latex], which is currently written in standard notation. How do you think it is expressed in scientific notation?

How to: Convert Numbers from Standard Notation to Scientific NotationAlthough scientific notation can look confusing, we can follow a few simple steps to convert numbers in standard notation to scientific notation.

  1. Count the number of places that the decimal point needs to be moved to the right or left so that the coefficient is between [latex]1[/latex] and [latex]9[/latex].
  2. Move the decimal point the appropriate number of places to the right or left, and adjust the power of [latex]10[/latex] accordingly.
  3. Write the result as the coefficient followed by [latex]x 10^n[/latex], where [latex]n[/latex] represents the number of times that the decimal point was moved.

Remember the sign on [latex]n[/latex] depends on if you are converting a small or large number to scientific notation. A rule to remember is if you move your decimal to the left [latex]n[/latex] is positive and if you move your decimal to the right [latex]n[/latex] is negative.

How to: Convert Numbers from Scientific Notation to Standard NotationTo convert from scientific notation to standard notation, we simply need to do the reverse of the steps given before.

  1. Write the coefficient and the power of [latex]10[/latex] separately.
  2. Move the decimal point in the coefficient the same number of places to the left or right as the power of [latex]10[/latex] suggests.
  3. Combine the coefficient and the decimal point to get the standard notation representation of the number.

Scientific Notation

You can view the transcript for “How to convert a number to scientific notation” here (opens in new window).
You can view the transcript for “Converting to Scientific Notation Examples!” here (opens in new window).
You can view the transcript for “Math Antics – Scientific Notation” here (opens in new window).