  This paper aims to introduce high school students to the intriguing world of
continued fractions, a mathematical concept that provides a unique
representation of numbers. The study focuses on the exploration and development
of the fundamental properties of both Finite and Infinite Continued Fractions.
It further delves into the computation of quadratic numbers using given
periodic continued fractions and the concept of conjugate quadratic numbers. A
significant part of the paper is dedicated to the approximation of real numbers
and the convergence properties of continued fractions. The study of continued
fractions offers a profound understanding of the intricate relationships within
number systems, a key emphasis in contemporary mathematics education. The paper
is designed to be engaging and interactive, fostering a fun and stimulating
learning environment. By the end of this study, students will have gained a
comprehensive understanding of continued fractions, their properties, and their
applications, thus enhancing their mathematical proficiency and problem-solving
skills. This paper serves as a stepping stone for students to explore more
complex mathematical concepts and theories, fostering a deeper appreciation for
the subject.
