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"very small fraction" is a correct and usable phrase in written English.
It can be used to describe a small amount or proportion within a larger context. Here is an example sentence: Only a very small fraction of the overall budget was allocated to research and development.
Exact(60)
I just like a very small fraction of this profession, which is the music.
"It only saved the lives of a very small fraction of them".
But Sean McCormack, the department's spokesman, said that of 1,800 escort missions by Blackwater this year, there had been "only a very small fraction, very small fraction, that have involved any sort of use of force".
The reports represented "a very small fraction" of the Xbox machines sold, a Microsoft spokeswoman, Molly O'Donnell, said.
All but a very small fraction of emigration, both legal and illegal, from Mexico is to the United States.
A very small fraction of this energy is caught, not by rock and wind and water, but by life.
Arabs mainly Muslims, as well as a number of Christians account for a very small fraction of the population.
That's still a very small fraction of the global meat market, which is estimated to be worth about $675bn by the US Meat Export Federation.
The Russians, however, agreed to double their contributions, but their dues are only a very small fraction of the American assessment.
Given Patagonia's sales figures, it is clear that the company repairs and recycles only a very small fraction of the number of products sold each year.
"But in the end, that a very small fraction of 1percentt of our users contacted us underscores, as always, the scale on which we do business".
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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