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The phrase "a very small slice" is correct and usable in written English.
You can use it to describe a tiny portion of something, whether literal or metaphorical.
Example: "In the grand scheme of things, my contribution to the project was just a very small slice of the overall effort."
Alternatives: "a tiny piece" or "a minuscule portion."
Exact(29)
"A very small slice of reality is exposed through the viewfinder".
I've got a very small slice of the pie, but it's mine.
Its modest broadcast stations enjoy robust profit margins but provide only a very small slice of the company's revenue.
"There's a very small slice of people who are genuinely undecided, but it's enough to win the presidency," said Rich Beeson, the political director for Mr. Romney's campaign.
Mr. DiDio said it would be "myopic" to believe "that servicing a very small slice of our audience is the way to go ahead".
It's turning off more than half the electorate that's not Cuban, and the people who would benefit from a change are a very small slice of the Cuban electorate.
Similar(30)
Be careful when digging up any sod around a tree; take very small "slices" off the top to ensure no root damage.
To increase resolution, we used a slow scan speed, a very small z slice interval and a small pinhole optimized to 1 airy unit.
It will be important to determine the extent to which very small slices (Ambady & Rosenthal, 1992) of professors' actions can forecast students' relational responses to specific professors.
This cake is very rich, so cut it into very small slices.
Clip 2 very small slices in each of the corners, making sure to not clip the seam you have just sewn.
More suggestions(18)
a very small fraction
a very small share
a very small bit
a very small cutting
a very small piece
a very tiny slice
a very little slice
a very small segment
a very modest slice
a very small stretch
a very narrow slice
a very small chunk
a very small interval
a very small ring
a very small niche
a very small paragraph
a very small circulation
a very similar slice
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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