What is the correct way of saying "third" in different contexts?

Question

What would be the correct way of saying "third" in the following contexts:

• Chronologically (This is the third time this happens)
• Ranked (I am the third best player in the world)
• Other? Maybe other context I haven't thought of that has meaning in Japanese but less in other languages?

Answer 1

You might know that every time numbers appear in Japanese, they are usually accompanied by a counter word, e.g. つ, 個, 回, 番, ...

To say "three items" you can say 3つ, "3 pieces" is 3個, "three times" is 3回, "number three" is 3番.

To make the number into an ordinal, e.g. "three" into "third", you simply add 目 as so

3つ目 third item
3個目 third piece
3番目 third [number]
3回目 third time

So, you example first example sentence become

これで3回目です。
This is the third time.

Alas, being n th place (e.g., in a tournament) already has its own counter. In Japanese, you don't need an ordinal, but just the counter 位{い}, so your second example becomes

私は世界3位の選手です。
I am the third best player in the world.

Answer 2

• Chronologically (This is the third time this happens)　→　3度目, 3回目
• Ranked (I am the third best player in the world)　→　(第)3位
• Other? Maybe other context I haven't thought of that has meaning in Japanese but less in other languages?　→　３つ目, 3番目, 第3番