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The phrase "approximately a fourth" is correct and usable in written English.
It can be used when you want to express a rough estimate of one-fourth of a quantity or amount.
Example: "The survey indicated that approximately a fourth of the participants preferred option A over option B."
Alternatives: "about a quarter" or "roughly one-fourth".
Exact(5)
Researchers also found that half of the water that reached the mixed layer originated from the Atlantic Ocean, while the Indian and Pacific oceans each contributed approximately a fourth.
Approximately a fourth of those who were admitted stayed for less than 24 h.
By contrast, approximately a fourth of Europe's total gas demand comes from Russia.
In two lineages, these variants reached high frequencies, comprising approximately a fourth of the population.
Under high LP, GTR accounted for approximately a fourth of all genes (25.09%), followed by TVM (15.7%), and TIM3 (14.98%).
Similar(55)
Approximately a third of all the shows were benched.
Approximately a third are participating for the first time.
This is still the way of life for approximately a third of Mongolians.
Injuries have forced Curry to miss approximately a third of the schedule so far.
We are approximately a third of the way through a decade of cuts.
Of these, approximately a third are deemed ineffective in some way.
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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