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Writing fractions as repeating decimals
Writing-fractions-as-repeating-decimals 256
Description
Exercise Name: Writing fractions as repeating decimals
Math Missions: 8th grade (U.S.) Math Mission, Arithmetic essentials Math Mission, Pre-algebra Math Mission, High school statistics and probability Math Mission
Types of Problems: 2

The Writing fractions as repeating decimals exercise appears under the 8th grade (U.S.) Math Mission, Arithmetic essentials Math Mission, Pre-algebra Math Mission and High school statistics and probability Math Mission. This exercise practices fluency between fractions and decimals.

Types of Problems

There are two types of problems in this exercise:

  1. Determine if it could be the number: This problem provides some information about a decimal and couple possible fractions. The user is to determine if each fraction could be the number, can't be the number, or must be the number.
    Wfard1

    Determine if it could be the number

  2. Recognize the repetition: This problem provides a fraction that may terminate or repeat (as all rational numbers do). The user is asked to give the first six truncated decimal places of the decimal and recognize the repeating part.
    Wfard2

    Recognize the repetition


Strategies

An ability to divide is all that is necessary for this problem.

  1. A calculator defeats the spirit, but can be used.
  2. When a decimal terminates, the repeating part is "0."
  3. Fractions that have only powers of two and five in the denominator terminate, all others have repetition.
  4. Make sure to truncate the decimal (cut off) rather than round.

Real-life applications

  1. This skill can be used to help approximate answers in science applications.
  2. Fractions are used in real life in many different ways, but they are most commonly used in the cooking, construction and science industries.

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