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The phrase "a very small increase" is correct and usable in written English.
It can be used when describing a minor change or growth in a particular context, such as statistics, measurements, or trends.
Example: "The report indicated a very small increase in sales over the last quarter, suggesting that the new marketing strategy is beginning to take effect."
Alternatives: "a slight increase" or "a minimal increase".
Exact(60)
This is a very small increase in risk".
A very small increase in resources would result in a huge explosion of activity.
That budget allowed for a very small increase in operating expenses.
There will be a very small increase in membership dues the first summer, and then it'll scale up over time".
"Over the last decade, there's been a very small increase, attributable to more people in the water," Mr. Paulos said.
The only significant change was a very small increase in first visits to specialists, especially for low back pain.
Only government activities showed a "very small" increase in growth, according to the Office for National Statistics, which released the figures this morning.
This all leads to a very small increase in safety.
Note that these two scenarios produce a very small increase in agricultural value added.
A very small increase in bulk density has increased the SOCS (Bolstad and Vose 2001).
BDCT, since this will reduce the bandwidth usage at the price of a very small increase of complexity.
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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