Correct spelling, explanation: this form is the correct one, because cardinal number three has irregular ordinal form: third. As we add suffixes from ordinal forms to numeral ordinal forms, the correct way to write forty-third as a number is 43rd, not
Definition of 43rd:
numeral, ordinal number between 42nd and 44th
He had starred in man films before, but only the newest one was when his career took off, and it was his 43rd role.
Jack got a trip around the world as a present for his 43rd birthday.
Incorrect spelling, explanation:
43th is an incorrect form of ordinal number forty-third, as the written form ends with suffix -rd, so does numeral form. Therefore the correct one will be 43rd. This is due to the fact, that numbers one, two and three are irregular and their ordinal forms are first, second and third. Thus the suffixes will be respectively -st, -nd and -rd, not -th as in other numbers.
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