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Exploring Zero and Negative Exponents in Scientific Notation

This lesson explores the meaning of non-positive exponents, how to rewrite expressions with negative exponents, and converting numbers to standard notation from scientific notation.

jamessjohnson
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Exploring Zero and Negative Exponents in Scientific Notation

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  1. Lesson 6.6: Zero and Negative Exponents To investigate the meaning of non-positive exponents. To write a number with a negative exponent in a form that has a positive exponent and write a number with a positive exponent in a form that has a negative exponent. To write in scientific notation numbers close to zero.

  2. Have you noticed that so far in this chapter the exponents have been positive integers? In this lesson you will learn what a zero or a negative integer means as an exponent.

  3. More Exponents • Step 1 • Use the division property of exponents to rewrite each of these expression with a single exponent.

  4. Some of your answers in Step 1 should have been positive exponents, some should have been negative, and some should have been zero exponents.

  5. Step 2 • How can you tell what type of exponent will result simply by looking at the original expression?

  6. Step 3 • Go back to the expressions in Step 1 that resulted in a negative exponent. Write each in expanded form. Then reduce them.

  7. Step 4 • Compare your answer from step 3 and Step 1. Tell what a base raised to a negative exponent means. • Step 5 • Go back to the expressions in Step 1 that resulted in an exponent of zero. Write each in expanded form. Then reduce them.

  8. Step 6 • Compare your answers from Step 5 and Step 1. Tell what a base raised to an exponent of zero means.

  9. Step 7 • Use what you have learned about negative exponents to rewrite each of these expressions with positive exponents and only one fraction bar.

  10. Step 8 • In one or two sentences, explain how to rewrite a fraction with a negative exponent in the numerator or denominator as a fraction with positive exponents.

  11. For any nonzero value of b and for any value of n,

  12. Example A • Use the properties of exponents to rewrite each expression without a fraction bar.

  13. Example B • Solomon bought a used car for $5,600. He estimates that it has been decreasing in value by 15% each year. • If his estimate of the rate of depreciation is correct, how much was the car worth 3 years ago? • If the car is 7 years old, what was the original price of the car?

  14. Example C • Convert each number to standard notation from scientific notation, or vice versa. • A pi meson, an unstable particle released in a nuclear reaction, “lives” only 0.000000026 seconds. • The number 6.67 x 10-11 is the gravitational constant in the metric system used to calculate the gravitational attraction between two objects that have given masses and are a given distance apart. • The mass of an electron is 9.1 x 10-31 kg.

  15. Example C • Convert each number to standard notation from scientific notation, or vice versa. • A pi meson, an unstable particle released in a nuclear reaction, “lives” only 0.000000026 seconds. • The number 6.67 x 10-11 is the gravitational constant in the metric system used to calculate the gravitational attraction between two objects that have given masses and are a given distance apart. • The mass of an electron is 9.1 x 10-31 kg.

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