Use 'tercentenary' when referring to 300 years since a particular event, not general time spans. The university is planning a conference for its tercentenary.
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Celebratory Context
Often used when planning or reporting celebrations of 300-year milestones. The tercentenary of the town's founding included a time capsule burial.
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Formal Occasions
Best suited for formal or official communications and writings. A tercentenary medal was commissioned for the occasion.