How to Write a Repeating Decimal as a Fraction

Learn how to convert repeating decimals into fractions (rational numbers) with this clear and concise tutorial from Mario's Math Tutoring! This video breaks down the step-by-step process for transforming repeating decimals, whether they repeat immediately or have a non-repeating part, into a ratio of integers. We'll use algebraic manipulation involving multiplication by powers of 10 and subtraction to isolate the repeating portion. Follow along with two detailed examples and discover how to check your work. Perfect for students looking to master this essential concept in rational numbers!

Timestamps:

0:00 - Introduction to Converting Repeating Decimals to Fractions
0:15 - Example 1: Converting 2.353535... to a Fraction
0:30 - Setting up the Equation (n = repeating decimal)
0:45 - Multiplying by a Power of 10 (based on repeating digits)
1:15 - Subtracting Equations to Eliminate Repeating Part
1:40 - Solving for 'n' and Simplifying the Fraction
2:00 - Writing as a Mixed Number or Improper Fraction
2:30 - Example 2: Converting 0.3121212... to a Fraction (Non-Repeating Part)
3:00 - Strategically Multiplying to Align Repeating Parts
4:00 - Subtracting Equations to Eliminate Repeating Part
4:30 - Solving for 'n' and Simplifying the Fraction
5:00 - How to Check Your Work (Calculator Verification)
5:25 - Conclusion and More Practice

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