Correct spelling, explanation: this form is the correct one, because ending for ordinal number second and any other number ending with second is nd (ending of the number in full-word form is an ending for numeral form). Therefore 32nd is the correct form (thirty-second). This is also why
32th is mistaken (th suffix is used for ordinal numbers ending with th in a word form). 32nd is the correct form.
Definition of 32nd:
numeral, ordinal number between 31st and 33rd
You should buy the newest, 32nd edition of this book. It’s an updated version.
My son was born on my 32nd birthday.
Incorrect spelling, explanation: this form is incorrect, because ending th is used only with the numbers which end with th in their word form, so for example sixth, twenty-fourth etc. The correct ending for thirty-second is therefore 32nd, not
32th. Nd ending in second points to 32nd as the correct form.
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