Zero and Negative Exponents

A Grain of Sand

You know that scientific notation is often used to represent very large numbers in order to make calculations less tedious to perform (for example, the distance between the Sun and Earth). For the same reason, scientific notation is also used to represent very small numbers (for example, the width of a strand of hair, the diameter of a blood cell, etc.). When performing calculations with numbers in scientific notation that represent very small values, you will notice negative exponents. Take a look at the following example.

The mass of a grain of sand is approximately 6.7 x 10^-4 grams. A decorative glass container holds approximately 4.32 x 10⁵² grains of sand. What is the approximate mass of the sand in the container? Write your answer in scientific notation.

mass of the sand in the container	=	mass of a grain of sand	·	number of grains of sand in the container
	=	6.7 x 10-4	·	4.32 x 1052

To multiply numbers in scientific notation, multiply the coefficients first. Then, multiply the powers by adding the exponents.

	=	6.7 · 4.32	·	10-4 · 1052
	=	(28.944)	·	(1048)

You determined the mass of the sand in the glass container is approximately 28.944 x 10⁴⁸ grams. You are not quite finished with the problem, however. Remember that for a number to be written in scientific notation, the coefficient must be greater than or equal to one, and less than ten. Because 28.944 is greater than ten, you will need to manipulate this value. You can accomplish this in two steps:

1. Decrease 28.944 by a power of ten, or in other words, move the decimal point one place to the left.
   
2. Increase the exponential portion by a power of ten, or in other words, increase the exponent by one.

You have determined that the mass of the sand in the container, in scientific notation, is 2.8944 x 10⁴⁹ grams.

 

Zero and Negative Exponents

Consider the expressions x⁰ and x^(-2). How would you simplify these expressions? In this interactivity, you will learn how to apply the Definition of a Zero Exponent and the Definition of a Negative Exponent to simplify exponential expressions. Click the player button to begin.

View a printable version of this interactivity.

 

Zero and Negative Exponents Review

Now that you have explored zero and negative exponents, it is time to review your knowledge and practice what you have learned. Click the player button to get started.

 

 

 

Did you answer the content review questions incorrectly? Do you want more instruction or extra practice? If so, view the videos Negative Exponents and Zero Exponents from eMediaVASM.