What is a 300th anniversary called?

Tercentenary is a 300th anniversary or its celebration.

Latin terms for anniversaries are mostly straightforward, particularly those relating to the first twenty years (1–20), or multiples of ten years (30, 40, 60, 70 etc.), or multiples of centuries or millennia (100, 200, 300, 1000, 2000, 3000, etc.) In these instances, the name of the anniversary is generally derived from the Latin word(s) for the respective number of years. However, when anniversaries relate to fractions of centuries (125, 150, 175, 250 years—i.e. 1.25, 1.5, 1.75, and 2.5 centuries), the situation is not as simple.

Roman fractions were based on a duodecimal system. From 1⁄12 to 8⁄12 they were expressed as multiples of twelfths (uncia "twelfth"; the source of the English words inch and ounce) and from 9⁄12 to 11⁄12 they were expressed as multiple twelfths less than the next whole unit—i.e. a whole unit less 3⁄12, 2⁄12 or 1⁄12 respectively. There were also special terms for quarter (quadrans), half (semis), and three-quarters (dodrans). Dodrans is a Latin contraction of de-quadrans which means "a whole unit less a quarter" (de means "from"; quadrans means "quarter". Thus for the example of 175 years, the term is a quarter century less than the next whole (bi)century or 175 = (−25 + 200).

In Latin, it seems that this rule did not apply precisely for 1½. While secundus is Latin for "second", and bis for "twice", these terms are not used such as in sesqui-secundus. Instead sesqui (or ses) is used by itself.