Lesson 29 — Repeating Decimals

🎯 Goal

Understand and represent decimals that repeat infinitely.

📖 Lesson Description

• A repeating decimal has one or more digits that repeat infinitely
• Notation: bar above repeating digit(s) (e.g., 0.333… = 0.\(overline{3}\)
• Can convert to fraction: 0.\(overline{3}\) = 1/3

🔎 Examples

• 0.\(overline{6}\) = 2/3
• 0.1\(overline{6}\) = 1/6
• 0.\(overline{142857}\) = 1/7

✏️ Practice

1. Convert 0.\(overline{3}\) to fraction
2. Convert 0.2\(overline{5}\) to fraction
3. Write 1/9 as a repeating decimal