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The phrase "a tiny increase in" is correct and usable in written English.
You can use it when discussing a small or minimal change in quantity, size, or degree.
Example: "The study showed a tiny increase in the average temperature over the past decade."
Alternatives: "a slight rise in" or "a minimal growth in".
Exact(36)
There was no meltdown and indeed even a tiny increase in the share of the vote.
Even a tiny increase in the dose of medication can have serious effects — especially in babies born prematurely.
An American trial reported that PSA screening brought a tiny increase in mortality, relative to a control group.
For the second year in a row, it would freeze aid to local governments, and it would allow only a tiny increase in school aid.
The SNP did well in the constituency section, gaining 6 seats with a tiny increase in share of the vote, but lost 12 seats on the top up.
But the study predicts that the inducements would cause only a tiny increase in production even if they were offered without some of the limitations now in place.
Similar(24)
Even such a tiny increase would be welcome in a nation where consumer prices have been flat or have fallen in every month but one since May 1998.
As New Mexican Dick Holland, the scientist who authored the paper describing these butterflies, wrote, "a very tiny increase in global temperature shall push this taxon into thin air, and give it no place to live".
In some markets that means a small price cut, in others a tiny increase.
For many people, this disillusionment meant not voting at all: turnout was estimated at 43 per cent, a tiny increase on the last European election in 2009, but a gain unlikely to convince the growing number of Eurosceptics of the democratic credentials of Brussels.
The good news is that Summers seems to understand that a tiny increase (e.g., 0.2 percentage points) in our long-term economic growth rate (over the CBO's pathetic 2.17% forecast) will have more impact upon federal government finances than any conceivable "grand bargain" to raise taxes and cut spending.
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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