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The phrase "about a fifteenth 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 proportions.
Example: "The project is about a fifteenth of the total budget allocated for the year."
Alternatives: "approximately one-fifteenth of" or "roughly a fifteenth of".
Exact(1)
The N.R.A.'s annual lobbying budget is around three million dollars, which is about a fifteenth of what, say, the National Association of Realtors spends.
Similar(59)
About a sixth of the population never returned.
They are about a sixth of the population.
About a third of them cost between $250 and $1,000.
About a third of Pennsylvanians disagreed.
This covered about a tenth of costs.
About a third of students are minorities.
About a third of them are fatal.
About a third of them were Democrats.
Pakistan controls about a third of Kashmir.
(A li is about a third of a mile).
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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