notes

1. Module 2 Lesson 14.notebook
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Lesson 14: Converting Rational Numbers to Decimals Using Long Division 11/23/15
Homework: Lesson 14 Problem Set #1 and 2
Exam 3 Wednesday 11/25/15
Integers Fluency Practice
1.) -9 + 5
2.) -9 + (-5)
3.) 9 + (-5)
4.) -60 + 23
5.) 4 - 10
6.) -4 - 10
7.) -4 - (-10)
8.) 4 - (-10)

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Integers Fluency Practice
9.) -5(6)
10.) -5(-6)
11.) 5(-6)
12.) -9(-1)
13.) -81
9
14.) -81
-9
15.) 81
-9
16.)

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Review
1.)
2.)
3.) I paid for 5 months of my gym membership and my
bank account changed $-240. What was the change each
month?

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Problem Set Solutions
0.04
3.3125
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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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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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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:

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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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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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