The book integrates ergodic theory with alternating series expansions for real numbers by applying ergodic theory to analyze the behavior of a specific alternating series expansion algorithm. This algorithm generates unique representations of real numbers as alternating series of rationals. By studying the ergodic properties of the transformation generating these series, the book explores the asymptotic behavior of the digits in the series representation. This integration has implications for computational mathematics, as it provides insights into the convergence and distribution of digits in number expansions, which can be useful in developing algorithms for numerical computations and understanding the complexity of computational problems. Additionally, it contributes to the field of metric number theory by providing a new perspective on the study of number expansions and their properties.