This paper introduces a novel approach for efficient searching of real numbers by integrating Fredman, Komlós and Szemerédi’s sparse table technique [4] with correspondence between real numbers and the integers converted from them. We achieve constant time searching capabilities while maintaining an O(n) storage bound. Through an exploration of comparison-based sorting algorithms and the conversion of real numbers into integers using Han’s algorithm [8], we establish a comprehensive framework capable of seamlessly handling both integers and real numbers. This research not only enhances the efficiency of searching operations but also contributes to the broader landscape of algorithmic optimization, providing a robust solution for real number searching within computational constraints.