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The phrase "a very tiny proportion of" is correct and usable in written English.
It can be used when discussing a small part or percentage of a larger whole, often in statistical or analytical contexts.
Example: "In the survey, a very tiny proportion of respondents indicated that they were dissatisfied with the service."
Alternatives: "a minuscule percentage of" or "a small fraction of".
Exact(3)
However, there is a sense in which the rational numbers form a very tiny proportion of the real numbers.
As a result, pollination by the moths makes up a very tiny proportion of all the pollinator visits that occur within that community and probably has little effect on plant reproduction or natural selection.
But that certainly is not possible now, Paternoster says: "The variability in this study only explains a very tiny proportion of the variability in face shape, and so cannot be used to predict the face shape".
Similar(57)
A very tiny glimmer of hope.
Everything starts with solving a very tiny slice of a problem.
Often, only a very tiny fraction of all these possible assignments participates in a satisfactory solution.
So for a very tiny dose of digoxin I was actually having the digoxin side effects... ........ (Interviewee 13).
Despite rigorous model selection procedures, in rare cases PAML may estimate very high levels of selection over a tiny proportion of a given sequence (even a single site), leading to greatly inflated average levels of dN/dS.
Because Alan Greenspan created a very high real cost of leverage earlier this year, only a tiny proportion of hedge funds engage in the sort of activity that might create real problems of counterparty defaults.
The death penalty hardly acts as a deterrent, since only a tiny proportion of murderers are arrested, tried and convicted.
The major obstacles in treatment development are that gene disease associations reveal very little about the underlying biology and that any implicated gene variant explains only a tiny proportion of an individual's overall risk for an AUD.
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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