taru-adjective, adverb taking the 'to' particle
accurate; exact; punctual; neat
Describes something done precisely, on time, or in an orderly manner. Often used adverbially with と.
彼は時間に正々としている。
He is punctual about time.
書類を正々と整理した。
I neatly organized the documents.
正確 is a more common and versatile word for 'accurate' or 'precise', used as a na-adjective or noun. 正々 is a literary, somewhat old-fashioned taru-adjective/adverb.
きちんと is a common everyday adverb for 'properly' or 'neatly'. 正々 is more formal and literary.
Reduplication of 正 (せい, 'correct, proper'), forming a taru-adjective/adverb. The exact historical derivation is uncertain, but the form follows a classical pattern for adverbial expressions.