🔑 Key Concepts
- Every repeating decimal is a rational number because it can be written as a fraction.
- If all digits after the decimal repeat, write the repeating digits over as many 9s as needed.
- If some digits do not repeat, separate the decimal into a terminating part and a repeating part.
- After writing the repeating decimal as a fraction, always simplify the result.
- Using a consistent algorithm makes longer repeating-decimal problems much easier to organize.
✏️ Worked Examples — Repeating Decimals to Fractions
🧠 Math Vocabulary
- Repeating Decimal: A decimal in which one or more digits continue in a pattern forever.
- Rational Number: A number that can be written as a fraction of two integers.
- Terminating Decimal: A decimal that ends.
- Numerator: The top number of a fraction.
- Denominator: The bottom number of a fraction.
- Simplify: Rewrite a fraction in lowest terms.
💡 Main Idea
Repeating decimals can always be written as fractions, which means they are rational numbers. When all digits repeat, the process is quick: write the repeating digits over as many 9s as needed, then simplify. When some digits do not repeat, it helps to separate the decimal into a terminating part and a repeating part, convert each piece to a fraction, and then combine the results.
📚 What You Should Already Know
Before this lesson, students should understand decimal place value, equivalent fractions, and how to simplify fractions. It also helps to know that some fractions produce terminating decimals while others produce repeating decimals.
🚀 What Comes Next
After learning how to convert repeating decimals into fractions, students can compare rational and irrational numbers more confidently, classify numbers within the real number system, and move back and forth between fractions and decimal representations with greater precision.
🧩 Embed This Video in Your LMS
Teachers can embed this YouTube video directly into Canvas, Google Classroom, Schoology, or another learning platform. Click below to show the embed code.