Final answer:
Approximately 77 years elapsed between Diocletian's Great Persecution in 303 C.E. and Emperor Theodosius's decree in 380 C.E. that marked the official transition of Rome to a Christian state, effectively suppressing pagan worship.
Step-by-step explanation:
The elapse of time between Diocletian's Great Persecution in 303 C.E. and Emperor Theodosius's prohibition of all forms of pagan worship spans a period of approximately 77 years. The Great Persecution began with Diocletian's attempt to wipe out Christianity by ordering the demolition of Christian buildings and execution of many Christians. Following this, the reign of Emperor Constantine brought significant change; after his conversion to Christianity, he passed the Edict of Milan in 313 C.E., guaranteeing religious tolerance, including the tolerance of Christianity. Finally, in 380 C.E., Emperor Theodosius I declared the Roman Empire a Christian state, effectively outlawing pagan worship. Therefore, the process of Christianity going from a persecuted religion to becoming the state religion of the Roman Empire took under a century.