Prefix used before a number to mean 'exactly that number' or 'precisely'. Common in formal or written contexts.
正午は正十二時です。
Noon is exactly twelve o'clock.
正午に門が閉まる。
The gate closes at noon.
noun which may take the genitive case particle 'no', noun
Archaic noun/adjectival use meaning 'correct' or 'true'. Not used in modern Japanese outside fixed expressions or historical contexts.
Archaic noun referring to the highest administrative position (長官) in the ritsuryō period. Historical term.
See also: 長官 (かみ)
I want to hear an honest answer.
In the ritsuryō system, Senior Third Rank was higher than Junior Third Rank.
The 正 was the highest of the four administrative positions in the ritsuryō system.
true identity; true form; true colors · consciousness; one's senses
front; facade; main entrance
New Year; New Year's (esp. first three days) · first month of the year; January
sanity; sound mind; consciousness; soberness
noon; midday
New Year (esp. first three days) · first month of the year; January
correct doctrine; orthodox sect
net; actual; full · net weight · net price; cost price · actual content; substantive part; useful part
revealing the truth; demonstrating the truth
midnight
correct practices; right conduct
center of a Noh stage · Shōchū era (1324.12.9-1326.4.26)
authentic text; original document
true dharma; true teachings of Buddha · age of the true law
judge of the Imperial Prosecuting and Investigating Office; judicial officer; minister of justice · Imperial Prosecuting and Investigating Office
official register; authenticated copy; play script
pure silk
high Buddhist priest; bishop (Buddhist)
right mindfulness · true faith (in rebirth in the Pure Land)
public storehouse for tax grain and valuables (ritsuryō system)
downstage center
right livelihood
direct retribution; body and mind resulting from karma
right concentration
guest of honor · main guest at a tea ceremony
seat of honor
correct meaning; original meaning · true heart; sincere intention
on the hour; exactly at the hour
price tag; price label
The kanji 正 carries the core meaning of 'correct' or 'proper'. The prefix use for 'exactly' before numbers is a natural extension. The archaic court rank and administrative uses are historical and not productive in modern Japanese.