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English ordinals take -st, -nd or -rd for numbers ending in 1, 2 or 3, and -th otherwise. The teens 11, 12 and 13 are exceptions and always take -th.
Suffix rule
ends 11–13 → th; else ends 1 → st, 2 → nd, 3 → rd, otherwise th
23rd, because it ends in 3 and is not in the 11–13 exception band.
Because its last two digits are 13, which falls in the teen exception.