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The phrase "about a sixth of" is correct and usable in written English.
It can be used when estimating or approximating a fraction of a whole, particularly in contexts involving measurements, quantities, or statistics.
Example: "About a sixth of the participants in the study reported feeling more energized after the intervention."
Alternatives: "approximately one-sixth of" or "roughly a sixth of".
Exact(60)
About a sixth of the population never returned.
Collectively, they account for about a sixth of global trade.
It's about a sixth of the mass of our Sun.
They are about a sixth of the population.
After all, manufacturing does account for about a sixth of the economy.
The contracts would cover 1,100 bus routes, about a sixth of the city's total.
About a sixth of those ages 16 to 24 pooh-poohed democracy in the mid-1990s.
Nassau and Suffolk Counties together now account for about a sixth of the overall state vote.
About a sixth of the campaign's 106 top fund-raisers — dubbed innovators and trailblazers — are lobbyists.
Melt some butter over medium heat, and then pour about a sixth of the batter into the pan.
She estimated that lawyers in town for the patent docket were responsible for about a sixth of her sales.
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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