Final answer:
The Han emperors introduced Confucian ideals and the Mandate of Heaven into their governance, creating a sense of continuity amongst dynasties and establishing a merit-based professional civil service.
Step-by-step explanation:
Han emperors changed the way China was ruled by incorporating Confucian ideals and a system of beliefs into their government. They saw themselves as "Sons of Heaven", ruling under the Mandate of Heaven, a core ideology that provided continuity among dynasties and a shared cultural identity for their subjects. This period also saw the solidification of a professional civil service, with scholar-officials selected through rigorous examinations, enhancing administrative stability and reducing the influence of hereditary nobles. The Song dynasty, in particular, made significant progress by reforming this process to be more meritocratic, greatly influenced by Confucian principles.