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Module 2 lesson 14

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  • 1. Module 2 Lesson 14.notebook Lesson 14: Converting Rational Numbers to Decimals Using Long Division November 20, 2013 11/20/13 Homework: Lesson 14 Problem Set and Quiz Friday Do Now: Exit Ticket 12 1
  • 2. Module 2 Lesson 14.notebook November 20, 2013 2
  • 3. Module 2 Lesson 14.notebook November 20, 2013 3
  • 4. Module 2 Lesson 14.notebook November 20, 2013 Homework Answers 4
  • 5. Module 2 Lesson 14.notebook November 20, 2013 Example 1: Can All Rational Numbers Be Written as Decimals? a. Using the division button on your calculator, explore various quotients of integers 1 through 11. Record your fraction representations and their corresponding decimal representations in the space below. b. What two types of decimals do you see? 5
  • 6. Module 2 Lesson 14.notebook November 20, 2013 Example 2: Decimal Representations of Rational Numbers In the chart below, organize the fractions and their corresponding decimal representations listed in example 1 according to their type of decimal. Terminating  What do these fractions have in common? Non-Terminating What do these fractions have in common? 6
  • 7. Module 2 Lesson 14.notebook November 20, 2013 Example 3: Converting Rational Numbers to Decimals Using Long-Division Use the long division algorithm to find the decimal value of 7
  • 8. Module 2 Lesson 14.notebook November 20, 2013 Exercise 1: Convert each rational number to its decimal form using long division a.  b.  8
  • 9. Module 2 Lesson 14.notebook November 20, 2013 Example 4: Converting Rational Numbers to Decimals Using Long-Division Use long division to find the decimal representation of 9
  • 10. Module 2 Lesson 14.notebook November 20, 2013 Question: What part of your calculation causes the decimal to repeat? 10
  • 11. Module 2 Lesson 14.notebook November 20, 2013 Exercise 2 Calculate the decimal value of the fraction below using long division. Express your answers using bars over the shortest sequence of repeating digits. a. b. c. d. 11
  • 12. Module 2 Lesson 14.notebook November 20, 2013 Exercise 2 Calculate the decimal value of the fraction below using long division. Express your answers using bars over the shortest sequence of repeating digits. a. b. c. d. 12
  • 13. Module 2 Lesson 14.notebook November 20, 2013 Example 5: Fractions Represent Terminating or Repeating Decimals How do we determine whether the decimal representation of a quotient of two integers, with the divisor not equal to zero, will terminate or repeat? If the remainder is zero: If the remainder is not zero: 13
  • 14. Module 2 Lesson 14.notebook November 20, 2013 Example 6: Using Rational Number Conversions in Problem Solving a. Eric and four of his friends are taking a trip across the New York State Thruway. They decide to split the cost of tolls equally. If the total cost of tolls is $8, how much will each person have to pay? b. Just before leaving on the trip, two of Eric's friends have a family emergency and cannot go. What is each person's share of the $8 toll now? 14
  • 15. Module 2 Lesson 14.notebook November 20, 2013 Closing: 1.) What should you do if the remainders of a quotient of integers do not seem to repeat? 2.) What is the form for writing a repeating decimal? 15
  • 16. Module 2 Lesson 14.notebook November 20, 2013 16