Relationship between magic fractions and decimals based on Lucas and Fibonacci numbers - โกวรรณ์ ธนิษฐา; บัวทอง พิมพ์กมล; ประทีปจิตต์ ศุภสิทธิ์ (ศวท : ศิลปศาสตร์ วิทยาศาสตร์และเทคโนโลยี (LAS: Liberal Arts, Science and Technology), 2026)
This research aims to study the relationship between fractions and decimals based on Lucas and Fibonacci sequences by considering the decimal values of fractions with digit numbers in the Lucas and Fibonacci sequences. We analyze the pattern of repeated decimals and their special properties. The results show the mathematical relationship and pattern between Lucas and Fibonacci sequences in the occurrence of the decimals. We give the exact number of Fibonacci numbers in decimal forms of remarkable fractions studied by James Smoak (2003). Our theorems may be applied in numerical analysis such as approximations and errors.