当用于特指的时候用定冠词the。

例:

I have won the first prize in the match.我在比赛中得了第一名。

序数词前面一般加定冠词表示“第……”之意,但在second、third等词前加不定冠词表示“又一,再一”之意。 

如: a second a third a fourth a fifth a sixth a seventh an eighth 

下句中“a first”表示“第一名、冠军”。

He is a top student in our class, he often gets a first in maths