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Exponent Rules & Scientific Notation

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This guide by Geoff Clement examines the fundamental rules of exponents and scientific notation, providing clear examples and applications. It emphasizes crucial assumptions like a ≠ 0 and b ≠ 0, exploring several fascinating examples including the copper content in a human body and IRS tax revenue calculations. Additionally, it discusses the definition of a light year, making complex concepts accessible. Whether you're reviewing or learning these mathematical principles, this resource is a valuable tool for students and educators alike.

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Exponent Rules & Scientific Notation

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  1. Exponent Rules & Scientific Notation Geoff Clement, July 2013

  2. “The Big Three” We assume a ≠ 0.

  3. Examples

  4. Examples

  5. Related Rules We assume a ≠ 0 and b ≠ 0.

  6. The Home Stretch We assume a ≠ 0 and b ≠ 0.

  7. Examples

  8. Examples

  9. A mixture of many of the rules . . .

  10. Scientific Notation We assume 1 ≤ a < 10 and b is an integer.

  11. Scientific Notation We assume 1 ≤ a < 10 and b is an integer.

  12. Fascinating Examples • The body of a 150-lb person contains 2.3 x 10–4 lb of copper. What percent of the person’s body weight is composed of copper?

  13. Fascinating Examples • In a recent tax year, the IRS averaged collecting $7,000 per person in the U.S. If the population of taxpayers in that year was 140,000,000, find the total revenue they collected.

  14. Fascinating Examples • 1 “light year” is defined as the distance light travels in one Earth year. The speed of light is roughly . Approximate the number of miles in a light year.

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