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Module 2 Lesson 9 Repeating Decimals.notebook
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September 21, 2016
HomeworkLesson 9
Problem set
Mid Module Test Tuesday
Sept. 21th
DO NOW:
Socrative Space Race
Module 2 Lesson 9 Repeating Decimals.notebook
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September 21, 2016
Problem Set Solutions
0.04
3.3125
4546
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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?
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Module 2 Lesson 9 Repeating Decimals.notebook
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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.
What do these fractions have in common? What do these fractions have in common?
Terminating Non-Terminating
The denominators are only divisible by factors of 2's and 5's.
The denominators are only divisible by another factor other than factors of 2's and 5's.
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Example 3: Converting Rational Numbers to Decimals Using Long-Division
Use the long division algorithm to find the decimal value of
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Exercise 1:
Convert each rational number to its decimal form using long division
a.
b.
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Module 2 Lesson 9 Repeating Decimals.notebook
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Example 4: Converting Rational Numbers to Decimals Using Long-Division
Use long division to find the decimal representation of 48
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What part of your calculation causes the decimal to repeat?
Question:
Module 2 Lesson 9 Repeating Decimals.notebook
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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.
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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.
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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:
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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?
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Module 2 Lesson 9 Repeating Decimals.notebook
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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?
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Lesson 9 Problem Set: Page 50
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Lesson 9 Problem Set: Page 51
