notes

1. Module 2 Lesson 9 Repeating Decimals.notebook
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September 21, 2016
Homework
Lesson 9
Problem set
Mid Module Test
Tuesday
Sept. 21th
DO NOW:
Socrative Space Race

2. Module 2 Lesson 9 Repeating Decimals.notebook
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September 21, 2016
Problem Set Solutions
0.04
3.3125
45­46

3. Module 2 Lesson 9 Repeating Decimals.notebook
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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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4. 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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5. Module 2 Lesson 9 Repeating Decimals.notebook
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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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6. Module 2 Lesson 9 Repeating Decimals.notebook
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Exercise 1:
Convert each rational number to its decimal form using long division
a.
b.
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7. 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
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What part of your calculation causes the decimal to repeat?
Question:

9. 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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10. Module 2 Lesson 9 Repeating Decimals.notebook
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September 21, 2016
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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11. Module 2 Lesson 9 Repeating Decimals.notebook
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September 21, 2016
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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12. Module 2 Lesson 9 Repeating Decimals.notebook
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September 21, 2016
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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13. 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

15. Module 2 Lesson 9 Repeating Decimals.notebook
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Lesson 9 Problem Set: Page 51