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The phrase "double the number" is correct and usable in written English.
You can use it when you want to indicate that the number should be multiplied by two. For example, "We need to double the number of volunteers we have for the fundraiser."
Exact(59)
This was more than double the number I had imagined.
That could roughly double the number of electric vehicles required.
That's more than double the number who ran in 2016.
The Kyl-Cantwell proposal would double the number.
That was more than double the number five years ago.
China today has 7,000 steel factories, double the number in 2002.
But the plan would also double the number of Class A shares.
The allocation will double the number of officers with high-powered weapons.
Officials say they plan to double the number of emergency demolitions to about 60 a week.
With his two surges, Obama will more than double the number of American troops in Afghanistan.
Last year 31,160 people sought asylum in Italy, more than double the number from 2007.
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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