What is the difference between one-third and one third?
In the following sentence,for example, which part is incorrect?
About one-third of the world's population uses chopsticks.

Question

Answer

Although both can be used, I think "one third" is less clear than "one-third", which links the two words together and makes it instantly clear that this is a fraction.
Instead of one-third, try replacing it with another fraction, say 8/19 and see how it looks.

Here's an example where the hyphen is dropped (determiner) :-
"Billy cut the pizza into three equal pieces. He gave one third to Amy, another third to Charlie, and the last third to Dave."

Answer

Written as "one-third", it is an adjective: I have a one-third interest in the company, meaning I own 33.33% of the company.

Written as "one third" it is a noun: one third of the people agree.

In your example it is a noun, so you write it without the hyphen: "one third"