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The phrase "a very small proportion" is correct and usable in written English.
It can be used when discussing a minor part or fraction of a whole in various contexts, such as statistics or research findings.
Example: "In the survey, a very small proportion of respondents indicated that they were dissatisfied with the service."
Alternatives: "a tiny fraction" or "a minimal percentage."
Exact(60)
A very small proportion get help from the NHS smoking cessation services.
A very small proportion (0.8%) of non-cancer related deaths were also associated with radiation.
"The Paralympics was actually about a very small proportion of the disabled population.
In addition the commission's terrorism or extremism cases remain a very small proportion of its investigatory activity.
The Guardian also blocks comments for legal reasons, but this makes up a very small proportion of blocked comments.
"In addition, only a very small proportion of those with severe disease are in these age groups.
"A very small proportion of their habitat will be potentially disturbed for a limited period of time," he said.
Contrary to popular opinion, asylum seekers make up a very small proportion of our immigrant population in the UK.
But a very small proportion, about 4%, have been killed by suicide bombers, whose victims have been mainly Afghan civilians.
They're the largest single group, but overseas students are a very small proportion of our total – 120 to 150.
Although ultraviolet light constitutes only a very small proportion of the total radiation, this component is extremely important.
More suggestions(16)
a very small amount
a very small incidence
a very tiny proportion
a very small ratio
a very little proportion
a very limited proportion
a very modest proportion
a very small figure
a very small population
a very minor proportion
a very small fraction
a very small representation
a very small share
a very small rate
a very small extent
a very small part
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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