SUMMARY
The discussion focuses on the mathematical technique for converting repeating, non-terminating decimals into fractional form, specifically using the example of x = 0.91919191. By multiplying by 100, the equation 100x - x = 91 illustrates that any periodic decimal can be expressed as a fraction, confirming that periodic decimals are rational numbers. The final result of this method is x = 91/99, providing a clear and concise representation of the original decimal.
PREREQUISITES
- Understanding of periodic decimals
- Basic algebraic manipulation skills
- Familiarity with rational numbers
- Knowledge of mathematical proofs
NEXT STEPS
- Study the properties of rational numbers and their decimal representations
- Explore techniques for converting other repeating decimals into fractions
- Learn about mathematical proofs related to number theory
- Investigate the implications of periodic decimals in real-world applications
USEFUL FOR
Students, educators, and anyone interested in understanding the conversion of repeating decimals to fractions and the underlying mathematical principles involved.