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The phrase "a very small fraction" is correct and usable in written English.
It can be used when referring to a tiny portion or percentage of a whole in various contexts, such as statistics or comparisons.
Example: "Only a very small fraction of the population participated in the survey, leading to inconclusive results."
Alternatives: "a tiny percentage" or "a minuscule part".
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".
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".
"With manual analysis we can de-anonymise a very small fraction of Tor users, however, no success de-anonymising a user... on demand".
More suggestions(16)
a very small component
a very small segment
a very small particle
a very small subset
a very small share
a very little fraction
a very small percentage
a very small slice
a very small aliquot
a very low fraction
a very minor fraction
a very small faction
a very small proportion
a very limited fraction
a very small niche
a very small paragraph
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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