Lesson 5.3

Exploring Repeating Decimals

ALCOS Standards

• PRE-ALGEBRA• DAILY PACING

GUIDE• 2ND QUARTER

12-14 8-3 4, 4a, 4b, 5, 5b

III-1, IV-2

V-1, V-2

Connected Math Moving Straight Ahead – Investigations 5.1

and 5.2

ARMT Standards 4 & 5

A87-A92

Objectives

1. Students will be able to distinguish between terminating and repeating decimals.

2. Students will be able to identify rational and irrational numbers.

3. Students will be able to convert decimals to fractions.

4. Students will be able to identify patterns in repeating decimals.

Problem of the Day

A) What are the decimal representations of 1/33, 2/33, 3/33, and 4/33?

B) Find other fractions with decimal representations the same as those of 1/33, 2/33, 3/33, and 4/33.

Answers to POD

A) 1/33=.030303…

2/33=.060606…

3/33=.090909…

4/33=.121212…

B) 2/66=.030303…

4/66=.060606…

6/66=.090909…

8/66=.121212…

Review-Problem 5.2

• Write each fraction as a decimal. Tell whether the decimal is terminating or repeating. If the decimal is repeating, tell which digits repeat.

A) 2/3 B) 3/8 C) 5/6 D) 35/10 E) 8/99

*Counting decimal places (power of 10) Place Value: Hands-on role play activity-Counting the

Ricehttp://arcytech.org/java/b10blocks/counting.html

Problem 5.2Answers:

A) 2/3 =0.666… R

B) 3/8 =0.375 T

C) 5/6 =0.8333… R

D) 35/10 =3.5 T

E) 8/99 =0.080808… R

Repeating Decimals

What is a fraction representation of the decimal 0.333…?

A) 3/10

B) 1/3

C) 33/100

*Journal: Explain how you got your answer and why the other two are incorrect.

Repeating Decimals

Correct answer:

B) 0.333… equals 1/3

Discuss journal entry.

Repeating Decimals

How could you write the decimal 0.454545… as a fraction?

Repeating Decimals

In today’s lesson, we will look for patterns that can help us write repeating decimals as fractions. Let’s begin working on the problem (5.3) and follow-up in pairs (pgs. 57-58).

Students will break off into pairs.

Explore

Problem 5.3

Page 57

A, B, C, D

*Transparency

Explore

*A fraction with a denominator of 9 has a decimal representation with a one-digit repeating pattern, or repetend, and the repetend is the number in the numerator.

*A fraction with a denominator of 99 has a decimal representation with a two-digit repetend:

a 0 followed by the number in the numerator if that number is less than 10; the number in the numerator if that number is equal to or greater than 10.

Explore

*A fraction with a denominator of 999 has a decimal representation with a three-digit repetend: two 0’s followed by the number in the numerator if that number is less than 10; one 0 followed by the number in the numerator if that number is equal to or greater than

10 but less than 1000; the number in the numerator if that number is equal to or greater than 100.

Explore

Problem 5.3 Follow Up

Page 58

1, 2, 3

Follow Up 5.3

Answers:

1. 1/99=0.0101…

2/99=0.0202…

3/99=0.0303…

A fraction with a denominator of 99 is equal to a repeating decimal. The repeating pattern has two digits.

Follow Up 5.3

2. 1/999=0.001001…

2/999=0.002002…

3/999=0.003003…

10/999=0.010010…

A fraction with a denominator of 999 is equal to a repeating decimal. The repeating pattern has 3 digits.

Follow Up 5.3

3. a) 0.333…=1/3

b) 0.050505…=5/99

c) 0.454545…=45/99

d) 0.045045…=45/999

e) 10.1212…=10 12/99

f) 3.999…=3 9/9, or 4

Repeating Decimals

• Discuss the patterns in the decimals.

*Question: What is the decimal representation for 19/9?

For 20/9?

*Write 19/9 as a mixed number.

*Write 20/9 as a mixed number.

Repeating Decimals

Question: What fraction is equivalent to 4.111111…?

Answer: (write as a fraction and mixed number)

Repeating Decimals

Answers:

4.111…=37/9

mixed number: 4 1/9

Rational / Irrational Numbers

Did you know? Refer to text page 58.

*http://www.eduplace.com/math/mathsteps/7/a/index.html

Rational/Irrational Numbers

Math Video Clip:

http://www.youtube.com/watch?v=OjjcF0t6CZ0

ACE Problems

Page 59 # 5 - 8Pages 61-62 # 26 - 30

Homework

ACE Problem #25

Assessment

Teacher Observation

Class Discussion / ACE Problems

Mathematical Reflections Page 63

Additional Resources/Activities

*Interactive Fractions to Decimals

http://www.learner.org/channel/courses/learningmath/number/session7/part_a/rings.html

*A Well Planned Diet

http://www.glencoe.com/sec/math/msmath/mac04/course2/webquest/unit3.php/

*Interactive activities: www.aplusmath.com/

*Interactive activities: www.aaamath.com/

*Interactive Baseball Game: http://www.funbrain.com/math/