1 Summer MA 15200 Lesson 3 Section P.2 (part 2) I Simplifying Using the Rules of Exponents The properties or rules of exponents are used to simplify exponential expressions. An exponential expression is simplified when • No parentheses appear. Use • No powers are raised to powers. Use • Each base occurs only once. Use • No negative or zero exponents appear. Use Use the steps above to simplify. Ex 1: Ex 2:2 Ex 3: Ex 4: Ex 5: True or False?3 Ex 6: Evaluate. II Writing Numbers in Scientific Notation A number is written in scientific notation when it is in the form where and n is an integer. If the original number is 10 or greater, the exponent of the base 10 will be positive. If the original number is less than 1, the exponent of the base 10 will be negative. If the original number is at least 1, but less than 10, the exponent of the base 10 will be zero. A positive exponent of 10 corresponds to a 10 or larger number. A negative exponent of 10 corresponds to a decimal number (less than 1). Ex 7: Write each standard number in scientific notation. a) It has been estimated that in the year 2020, the world population will be approximately 7,516,000,000 (Source: U.S. Bureau of the Census, International Data Base) b) A grain of sand has a mass of 0.0648 grams. Ex 8: Write each scientific notation number as a standard number. a) The lightest known particle in the universe, a neutrino has a maximum mass of kg. (Source: Guinness Book of World Records, 2004) b) A ton of 5-dollar bills is worth .4 III Computations with Scientific Notation • Multiply or Divide the Numeral parts. • Use the Product or Quotient Rules of Exponents with the base 10. • ‘Re-adjust’ if necessary to write number in scientific notation. • If directed, convert scientific notation to a standard decimal number. Ex 9: Use scientific notation to simplify these computations. Write answers in scientific notation and in decimal notation. a) b) c) d)5 Ex 10: Use scientific notation to solve these application problems. a) The mass on one proton is 1.67248 gram. Find the mass of one billion of these protons. b) A sheet of plastic shrink wrap has a thickness of 0.00015 mm. The sheet is 1200 mm by 79 mm. Find the volume of the sheet in cubic mm. c) In a certain country, taxes for 2008 of were collected. If there were 244 million people, what was the average amount of taxes per person? Round to the nearest thousandth in scientific notation and convert that number to a standard decimal
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