Exploring Repeating Decimals

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Lesson 5.3

• Exploring Repeating Decimals

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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
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Objectives

• 1. Students will be able to distinguish between
  terminating and repeating decimals.
• 2. Students will be able to identify rational
  and irrational numbers.
• Students will be able to convert decimals to
  fractions.
• Students will be able to identify patterns in
  repeating decimals.

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Problem of the Day

• What are the decimal representations of 1/33,
  2/33, 3/33, and 4/33?
• Find other fractions with decimal representations
  the same as those of 1/33, 2/33, 3/33, and 4/33.

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Answers to POD

• 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

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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 Rice
• http//arcytech.org/java/b10blocks/counting.html

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Problem 5.2

• Answers
• 2/3 0.666 R
• 3/8 0.375 T
• 5/6 0.8333 R
• 35/10 3.5 T
• 8/99 0.080808 R

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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.

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Repeating Decimals

• Correct answer
• B) 0.333 equals 1/3
• Discuss journal entry.

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Repeating Decimals

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

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Repeating Decimals

• In todays lesson, we will look for patterns that
  can help us write repeating decimals as
  fractions. Lets begin working on the problem
  (5.3) and follow-up in pairs (pgs. 57-58).
• Students will break off into pairs.

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Explore

• Problem 5.3
• Page 57
• A, B, C, D
• Transparency

13
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.

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Explore

• A fraction with a denominator of 999 has a
  decimal representation with a three-digit
  repetend two 0s 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.

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Explore

• Problem 5.3 Follow Up
• Page 58
• 1, 2, 3

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Follow Up 5.3

• Answers
• 1/990.0101
• 2/990.0202
• 3/990.0303
• A fraction with a denominator of 99 is equal to a
  repeating decimal. The repeating pattern has two
  digits.

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Follow Up 5.3

• 1/9990.001001
• 2/9990.002002
• 3/9990.003003
• 10/9990.010010
• A fraction with a denominator of 999 is equal to
  a repeating decimal. The repeating pattern has 3
  digits.

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Follow Up 5.3

• a) 0.3331/3
• b) 0.0505055/99
• c) 0.45454545/99
• d) 0.04504545/999
• e) 10.121210 12/99
• f) 3.9993 9/9, or 4

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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.

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Repeating Decimals

• Question What fraction is equivalent to
  4.111111?
• Answer (write as a fraction and mixed number)

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Repeating Decimals

• Answers
• 4.11137/9
• mixed number 4 1/9

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Rational / Irrational Numbers

• Did you know? Refer to text page 58.
• http//www.eduplace.com/math/mathsteps/7/a/index.
  html

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Rational/Irrational Numbers

• Math Video Clip

http//www.youtube.com/watch?vOjjcF0t6CZ0
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ACE Problems

• Page 59 5 - 8
• Pages 61-62 26 - 30

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Homework

• ACE Problem 25

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Assessment

• Teacher Observation
• Class Discussion / ACE Problems
• Mathematical Reflections Page 63

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Additional Resources/Activities

• Interactive Fractions to Decimals
• http//www.learner.org/channel/courses/learningmat
  h/number/session7/part_a/rings.html
• A Well Planned Diet
• http//www.glencoe.com/sec/math/msmath/mac04/cours
  e2/webquest/unit3.php/
• Interactive activities www.aplusmath.com/
• Interactive activities www.aaamath.com/
• Interactive Baseball Game http//www.funbrain.co
  m/math/