Lesson 45: Repeating & Terminating Decimals

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• Lesson Description
• Learning Objectives
• Topics Covered
• Key Terms
• Lesson Examples
• Practice Problems
• Tips & Common Mistakes
• Summary
• Challenge Problems
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Lesson Objectives

• Differentiate between repeating and terminating decimals.
• Convert fractions into decimals and identify their type.
• Recognize patterns in repeating decimals.
• Apply knowledge of decimal types to solve problems.

Introduction

Decimals can either terminate (end) or repeat a pattern indefinitely. Understanding the difference helps in calculations, rounding, and recognizing fraction equivalents.

Examples

Terminating Decimals

1/4 = 0.25 → ends after two digits.

Repeating Decimals

1/3 = 0.333… → the digit 3 repeats indefinitely.

7/6 = 1.1666… → 6 repeats after the decimal point.

Practice Problems

1. Convert 2/5 to a decimal. Is it terminating or repeating?
2. Convert 1/7 to a decimal. Identify the repeating pattern.
3. Convert 5/8 to a decimal. Terminating or repeating?
4. Write 0.272727… as a fraction.

Summary

Terminating decimals end after a finite number of digits, while repeating decimals continue indefinitely with a repeating pattern. Recognizing these patterns is key when converting between fractions and decimals.