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The phrase "a third believes" is correct and usable in written English.
It can be used when discussing the opinions or beliefs of a specific portion of a group, typically in surveys or studies.
Example: "In the recent survey, a third believes that climate change is the most pressing issue of our time."
Alternatives: "one-third thinks" or "a third of respondents feel".
Exact(2)
Just over a half of British respondents in the Ipsos survey have sympathy for refugees coming to Europe (up three points on October), a third believes that refugees should not count towards the government's immigration targets and 28% say that Britain has responded well to the refugee crisis (also up three points on last month).
According to a recent victimization poll, more than half of all Brazilians are "very afraid" of being killed, and almost a third believes they could be murdered in the next 12 months.
Similar(58)
Only a third believed death certificates to be accurate.
More than a third believe insurers often offer a price that can be reduced through haggling.
Barely a third believe the country is heading in the right direction.
Only 9% are consistent atheists and more than a third believe in life after death.
Just a third believe they are compatible with the "British way of life".
Polls show nearly half of Britons think "there are too many Muslims", and over a third believe Muslims pose a serious threat to democracy.
Only about a third believed that racial bias was a factor or that Zimmerman would have been arrested if the person he shot was white.
As the Press Association reports, a survey carried out by Ipsa also found more than a third believe they should keep generous final salary pensions.
Health educators themselves are no more clear: a survey last year found that nearly a third believed that oral sex was abstinent behavior.
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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