Module 2 lesson 14

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Module 2 lesson 14

  1. 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. 2. Module 2 Lesson 14.notebook November 20, 2013 2
  3. 3. Module 2 Lesson 14.notebook November 20, 2013 3
  4. 4. Module 2 Lesson 14.notebook November 20, 2013 Homework Answers 4
  5. 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. 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. 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. 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. 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. 10. Module 2 Lesson 14.notebook November 20, 2013 Question: What part of your calculation causes the decimal to repeat? 10
  11. 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. 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. 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. 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. 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. 16. Module 2 Lesson 14.notebook November 20, 2013 16

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