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The phrase "a third participated" is correct and usable in written English.
It can be used to indicate that one-third of a group or population took part in an activity or event.
Example: "In the survey, a third participated, providing valuable insights into consumer behavior."
Alternatives: "one-third took part" or "33% engaged".
Exact(1)
One Guatemalan Army officer on the C.I.A. payroll, the panel said, "ordered and planned assassinations of political opponents," a second took part in "assassinations or assassination attempts," and a third "participated in assassination, extrajudicial killing and kidnapping".
Similar(59)
In addition, members average about 50 minutes/month on the site with a third participating in over 30 of the platform's activities.
One co-moderator participated in the first two groups while a second participated in the third group.
The only exclusion criterion was having already participated in the study (e.g., if a participant presented to a second participating clinic).
In the event of the absence or incapacity of the secretary, the record may be authenticated by a second participating member of the review board.
The reliability of the readings was estimated by measuring intra-observer and inter-observer agreements (intraclass correlation) within a limited sample of radiographs and a second participating radiologist.
Secure audio files from a second participating centre were accessed to allow for detailed post-hoc analysis of 6x simulation 'debriefs'debriefs
But only a fourth participates in primaries.
The Egyptian Olympic Committee was founded in 1910, and an Egyptian first participated in the Summer Games in 1912.
Third, participating physiotherapists attend a general meeting.
Australia has competed in every modern Summer Olympics, winning its first two medals in 1896, five years before it even existed as a country; it first participated in the Winter Games in 1936.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com