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The phrase "across a number" is correct and usable in written English.
It can be used when referring to a range or variety of items, instances, or categories.
Example: "The study examined the effects of the new policy across a number of different sectors."
Alternatives: "over several" or "through various".
Exact(60)
Smith can also put across a number.
This pattern held across a number of statistical analyses.
They made a few mistakes over the last few weeks – across a number of different things.
Over 5.3m app downloads - audiences continue to consume the Guardian across a number of platforms.
"We are introducing across a number of government activities payments by result.
The report found that Australia was above average across a number of measures.
Mullah Omar, however, has proved stubborn and intractable across a number of years and settings.
Robots have already been put to work across a number of industries.
Its French subsidiary, created in 1990, employs 400 people across a number of sites.
"Old, fragile IT systems are a feature across a number of banks, not just RBS.
"That conclusion leaps across a number of chasms of scientific evidence".
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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