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The phrase "the total number" is correct and can be used in written English.
Example: The total number of students enrolled in the university has increased by 10% this year.
Exact(57)
I looked at the total number.
The total number of lines is variable.
The total number could be higher.
The total number sold is unknown.
The total number can be debated.
The total number in Darayya so far is 400 bodies.
The total number of wounded was around 350, he said.
The total number of books printed in 2014 was 123m.
The total number of the woman's children: 17.
Unaffiliated voters outnumber the total number of Democrats and Republicans.
The total number of MPs can be adjusted to compensate.
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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