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The phrase "a small small fraction of" is not standard in written English, as the repetition of "small" is unnecessary.
You can use it in informal contexts, but it may come across as awkward or redundant.
Example: "Only a small small fraction of the population is aware of this issue."
Alternatives: "a tiny fraction of" or "a small portion of".
Exact(2)
He adds: "A small, small fraction of Herbalife products are actually sold on eBay".
(On Herbalife's call with analysts and investors on Thursday, Des Walsh, the president, said that eBay prices were not a proxy for market prices. "Most people I know use eBay to buy branded products at a discount price," he said. "A small, small fraction of Herbalife products are actually sold on eBay").
Similar(58)
Due to the fact that dwarf males may readily establish in high numbers on a small area, a small fraction of migrants is enough to ensure gene flow between colonies or even populations.
We found that genes expressed in the node, because it is a small tissue and represents a small fraction of the total RNA, were difficult to detect by differential expression levels.
In [9], similar values were used for weighting regarding the floor-plans: a probability of zero (actually a very small value to allow a small fraction of particles to cross walls in the case of very inaccurate measurements or particle depletion) is applied when a particle's displacement crosses a wall.
Did I really want to fight my way to the head of the line just to ride a small fraction of a small mountain?
Enabling millions of students, young and old, full-time and part-time, undergraduate and postgraduate, to benefit from higher education is where the heavy lifting of social mobility is carried out, up and down the country and across the whole sector, not just in a small part of it for a small fraction of the population.
The fact that a small fraction of a small proportion of students will benefit from the campaign prompted criticism from Melissa Benn, the author of "School Wars: The Battle for Britain's Education" and a prominent advocate for state education.
Impact excitation of erbium and thus electroluminescence can be achieved in tunnelling diodes, although at very small excitation volume, which would cover only a small fraction of a wave guide.
by only a small fraction of a point.
This is usually a small fraction of a second.
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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