Table of Contents |
One application of exponent properties comes from scientific notation. Scientific notation is used to represent really large or really small numbers. An example of really large numbers would be the distance that light travels in a year measured in miles. An example of really small numbers would be the mass of a single hydrogen atom in grams. Doing basic operations such as multiplication and division with these numbers would normally be very cumbersome. However, our exponent properties make this process much simpler.
First, we will take a look at what scientific notation is. Scientific notation has two parts: a number between one and ten (it can be equal to one, but not ten), and a power of ten (10 raised to an exponent power).
Keeping this in mind, we can easily make conversions between standard notation and scientific notation.
EXAMPLE
Convert to scientific notation | Put decimal after first nonzero number |
Count how many times you have to move the decimal to obtain the original number | |
Exponent is how many times decimal moved, 4 | |
Positive exponent, standard notation is big | |
Our Solution |
EXAMPLE
Convert to scientific notation | Put decimal after first nonzero number |
Count how many times you have to move the decimal to obtain the original number | |
Exponent is how many times decimal moved, 3 | |
Negative exponent, standard notation is small | |
Our Solution |
Let's look at a few more examples.
Standard Notation | Scientific Notation |
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We can use similar thinking to convert from a number written in scientific notation into standard notation. For these types of conversions, remember that a positive exponent means a large number, and a negative exponent means a small number.
EXAMPLE
Convert to standard notation | Positive exponent means standard notation big number. Move decimal to the right 5 places |
Simplify solution with any commas | |
Our Solution |
EXAMPLE
Convert to standard notation | Negative exponent means standard notation is a small number. Move decimal to the left 3 places |
Simplify solution | |
Our Solution |
Source: ADAPTED FROM "BEGINNING AND INTERMEDIATE ALGEBRA" BY TYLER WALLACE, AN OPEN SOURCE TEXTBOOK AVAILABLE AT www.wallace.ccfaculty.org/book/book.html. License: Creative Commons Attribution 3.0 Unported License