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The phrase "about a tenth of" is correct and usable in written English.
It can be used when estimating or approximating a fraction of a whole, typically in numerical or statistical contexts.
Example: "The survey indicated that about a tenth of the participants preferred option A over option B."
Alternatives: "approximately one-tenth of" or "roughly ten percent of".
Exact(59)
So our total message length is about a tenth of a kilobyte (.13671875 Kbytes).
[Now] you can experiment at a cost of about a tenth of what it was a decade ago," Hochberg said.
This covered about a tenth of costs.
These account now for about a tenth of new mortgages.
The drop takes about a tenth of a second.
About a tenth of a second, Seaward calculated.
It lasted about a tenth of a second.
It contains about a tenth of the world's deposits of rare-earth minerals.
The 1901 document itself accounts for only about a tenth of this.
"Renewables have constituted only about a tenth of a percent," the report says.
Now about a tenth of confined young people are in an adult prison or jail.
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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