Bar Notation: Taming Repeating Decimals

PreAlgebra Grades High School 2:54 Video
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Lesson Description

Learn how to write repeating decimals using bar notation, a shorthand method for representing infinitely repeating digits.

Video Resource

How to Write Repeating Decimals Using Bar Notation | Math with Mr. J

Math with Mr. J

Duration: 2:54
Watch on YouTube

Key Concepts

  • Repeating decimals
  • Bar notation
  • Representation of rational numbers

Learning Objectives

  • Students will be able to identify repeating decimals.
  • Students will be able to write repeating decimals using bar notation correctly.
  • Students will be able to differentiate between repeating and non-repeating decimals.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of a decimal and different types of decimals (terminating, repeating, non-repeating). Briefly discuss why repeating decimals pose a notational challenge.
  • Video Viewing (7 mins)
    Watch the 'How to Write Repeating Decimals Using Bar Notation | Math with Mr. J' video. Encourage students to take notes on the examples provided.
  • Guided Practice (10 mins)
    Work through additional examples on the board, similar to those in the video. Emphasize the placement of the bar over the repeating digit(s). Include examples with single and multiple repeating digits, as well as cases where only some digits repeat.
  • Independent Practice (10 mins)
    Provide students with a worksheet containing a variety of repeating decimals. Students should convert these decimals into bar notation. Circulate to provide assistance as needed.
  • Wrap-up & Assessment (8 mins)
    Review the key concepts and answer any remaining questions. Administer the multiple-choice and fill-in-the-blank quizzes.

Interactive Exercises

  • Decimal Sort
    Create a set of cards with different types of decimals (terminating, repeating, non-repeating). Have students sort the cards into the correct categories.
  • Bar Notation Challenge
    Present students with increasingly complex repeating decimals and challenge them to write them correctly using bar notation.

Discussion Questions

  • Why is bar notation a useful tool for representing repeating decimals?
  • How does bar notation help us distinguish between repeating and non-repeating decimals?
  • What happens if you put the bar notation over digits that don't repeat in a decimal?

Skills Developed

  • Number sense
  • Symbolic representation
  • Attention to detail

Multiple Choice Questions

Question 1:

What does the bar in bar notation indicate?

Correct Answer: The digit repeats infinitely.

Question 2:

How would you write 0.7777... using bar notation?

Correct Answer: 0.7̅

Question 3:

Which number is equivalent to 0.121212...?

Correct Answer: 0.12̅

Question 4:

In the number 3.1454545..., which digits repeat?

Correct Answer: 45

Question 5:

What is the correct bar notation for 5.23333...?

Correct Answer: 5.23̅

Question 6:

Which of the following is a repeating decimal?

Correct Answer: 0.333...

Question 7:

Which decimal has a bar notation of 0.4̅?

Correct Answer: 0.444...

Question 8:

What does it mean when a decimal is repeating?

Correct Answer: It continues infinitely with a pattern.

Question 9:

How would you write the number 7.125125125... using bar notation?

Correct Answer: 7.125̅

Question 10:

What is the best way to represent 0.6666...?

Correct Answer: 0.6̅

Fill in the Blank Questions

Question 1:

A decimal that repeats infinitely has a special notation called ______ notation.

Correct Answer: bar

Question 2:

In bar notation, the ______ is placed over the digit or digits that repeat.

Correct Answer: bar

Question 3:

The decimal 0.8888... can be written in bar notation as 0.______.

Correct Answer: 8̅

Question 4:

The number 2.454545... can be represented using bar notation as 2.______.

Correct Answer: 45̅

Question 5:

If only the digit 6 repeats in the decimal 0.16666..., we write it as 0.1______.

Correct Answer: 6̅

Question 6:

Decimals that don't terminate or repeat are called ________ decimals.

Correct Answer: irrational

Question 7:

Bar notation provides a _______ way to write repeating decimals.

Correct Answer: shorter

Question 8:

The decimal 9.272727... using bar notation would be written as 9._______.

Correct Answer: 27̅

Question 9:

In the number 10.3333..., only the digit ______ repeats.

Correct Answer: 3

Question 10:

When several digits repeat in a sequence, the bar is placed over the _______ repeating group of digits.

Correct Answer: entire

Educational Standards

PA.N.1:[Standard] Read, write, compare, classify, and represent real numbers, and use them to solve problems in various contexts. PA.N.1.4:[Objective] 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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