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The phrase "a very high number" is correct and usable in written English.
It can be used when referring to a quantity that is significantly large in comparison to others.
Example: "The survey revealed that a very high number of participants preferred online shopping over traditional retail."
Alternatives: "an extremely large amount" or "a significantly high figure".
Exact(60)
"Real returns on both stocks and bonds inside and outside the U.S. was therefore 5%–a very high number!" Osbon says.
Real returns therefore on both stocks and bonds inside and outside the U.S. were therefore about 5%–a very high number!
I think it's a very high number".
"It is a very high number indeed".
We have a very high number of five-year-olds.
"We recognize that it's a very high number," said Senator Mary L. Landrieu, Democrat of Louisiana.
"Europe currently receives a very high number of refugees," Denmark's integration ministry defended the law.
There have been well over 100,000 hits on the blacklist campaign's Web site, a very high number for Japan.
The 40 critically injured victims was "a very high number, much higher than we normally encounter," Chief Rueda said.
"Asia has a very high number of people with mobile phones and with diabetes," Mr. Hendel said.
But this success seems to be falling apart amid a very high number of dropouts and poor-quality schooling for some of those who complete primary school.
More suggestions(15)
a very high incidence
a very high prevalence
a very considerable number
a quite high number
a very high availability
a very substantial number
a very aggressive number
a very easy number
a very few number
a very high probability
a very high price
a very manageable number
a very confusing number
a very high degree
a very low number
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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