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The phrase "about a fifth of" is correct and usable in written English.
It can be used when estimating or approximating a quantity that represents one-fifth of a whole.
Example: "About a fifth of the participants in the survey reported feeling satisfied with the service."
Alternatives: "approximately one-fifth of" or "roughly 20 percent of".
Exact(60)
Indonesia spends about a fifth of its budget on them.
Visible is only about a fifth of his book collection".
Only about a fifth of Americans favour this.
About a fifth of the residents are Hispanic.
(Today SBI has about a fifth of the banking market).
They made up about a fifth of the electorate.
(Actually, it would take about a fifth of a second).
(About a fifth of online daters are married men).
Npower accounts for about a fifth of RWE's sales.
About a fifth of the season is already gone.
(And that's after about a fifth of the babies miscarry).
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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