Taming Terminating and Repeating Decimals!

PreAlgebra Grades High School 5:40 Video
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Lesson Description

Learn the difference between terminating and repeating decimals with clear examples and practice problems.

Video Resource

Repeating and Terminating Decimals | Math with Mr. J

Math with Mr. J

Duration: 5:40
Watch on YouTube

Key Concepts

  • Terminating Decimals: Decimals that end.
  • Repeating Decimals: Decimals with a repeating pattern.
  • Fractions to Decimals: Converting fractions into decimals to determine if they terminate or repeat.

Learning Objectives

  • Students will be able to define terminating decimals and provide examples.
  • Students will be able to define repeating decimals and provide examples.
  • Students will be able to convert simple fractions to decimals and classify them as terminating or repeating.

Educator Instructions

  • Introduction (5 mins)
    Begin by asking students what they already know about decimals. Briefly review the concept of place value in decimals.
  • Video Viewing (10 mins)
    Play the "Repeating and Terminating Decimals | Math with Mr. J" video (https://www.youtube.com/watch?v=Jf_-FfaMMZM). Encourage students to take notes on the definitions and examples provided.
  • Discussion (10 mins)
    Facilitate a class discussion to reinforce the concepts. Use the discussion questions below to guide the conversation.
  • Interactive Exercises (15 mins)
    Have students work on the interactive exercises to practice identifying and converting decimals.
  • Wrap-up (5 mins)
    Summarize the key concepts and answer any remaining questions. Preview the upcoming topic (e.g., converting repeating decimals to fractions).

Interactive Exercises

  • Decimal Sort
    Provide students with a list of decimals (e.g., 0.25, 0.333..., 0.75, 0.121212..., 0.5). Have them sort the decimals into two categories: Terminating and Repeating.
  • Fraction Conversion
    Give students a list of fractions (e.g., 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/9, 1/10). Have them convert each fraction to a decimal and classify it as terminating or repeating.

Discussion Questions

  • What is the main difference between a terminating and a repeating decimal?
  • Can you give an example of a fraction that results in a terminating decimal? Why does it terminate?
  • Can you give an example of a fraction that results in a repeating decimal? Why does it repeat?
  • How can you tell if a fraction will result in a repeating or terminating decimal without doing the division?

Skills Developed

  • Critical Thinking
  • Problem Solving
  • Number Sense

Multiple Choice Questions

Question 1:

Which of the following is a terminating decimal?

Correct Answer: 0.75

Question 2:

Which of the following is a repeating decimal?

Correct Answer: 0.666...

Question 3:

The decimal representation of 1/3 is:

Correct Answer: 0.333...

Question 4:

The decimal representation of 1/4 is:

Correct Answer: 0.25

Question 5:

A decimal that ends is called a:

Correct Answer: Terminating decimal

Question 6:

A decimal that has a repeating pattern is called a:

Correct Answer: Repeating decimal

Question 7:

Which fraction will result in a terminating decimal?

Correct Answer: 1/8

Question 8:

Which fraction will result in a repeating decimal?

Correct Answer: 1/9

Question 9:

0.875 is an example of a(n) ___________ decimal.

Correct Answer: Terminating

Question 10:

0.1666... is an example of a(n) ___________ decimal.

Correct Answer: Repeating

Fill in the Blank Questions

Question 1:

A decimal that stops is called a ___________ decimal.

Correct Answer: terminating

Question 2:

A decimal that repeats forever is called a ___________ decimal.

Correct Answer: repeating

Question 3:

The fraction 1/5, when written as a decimal, is ___________.

Correct Answer: 0.2

Question 4:

The fraction 2/3, when written as a decimal, is ___________.

Correct Answer: 0.666...

Question 5:

The decimal 0.125 is a ___________ decimal.

Correct Answer: terminating

Question 6:

The decimal 0.444... is a ___________ decimal.

Correct Answer: repeating

Question 7:

When dividing to find the decimal equivalent of a fraction, if the remainder becomes zero, the decimal will __________.

Correct Answer: terminate

Question 8:

When dividing to find the decimal equivalent of a fraction, if the remainder repeats, the decimal will __________.

Correct Answer: repeat

Question 9:

The fraction 3/4 converts to the ___________ decimal.

Correct Answer: 0.75

Question 10:

1/6 written as a decimal is 0.1__________...

Correct Answer: 666

Educational Standards

PA.N.1:Read, write, compare, classify, and represent real numbers, and use them to solve problems in various contexts. PA.N.1.4:Compare and order real numbers; locate real numbers on a number line. Identify the square roots of perfect squares to 400 or, if it is not a perfect square root, locate it as an irrational number between two consecutive positive integers.

Teaching Materials

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