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The phrase "a much higher number" is grammatically correct and usable in written English.
The phrase can be used when referring to a value that has increased significantly. For example, "Last year, the company's profits were $1 million, but this year they increased to a much higher number--$5 million."
Exact(59)
If that changes, the company could face a much higher number of lawsuits.
"Now at a big club, that 20percentt is going to be a much higher number.
Officials estimate there will be a much higher number of fatal fentanyl-related overdoses in 2017.
Some of the white jurors had pressed for a much higher number.
However, a much higher number of bats were reported to have been killed by wind turbines.
They found a much higher number of snorers in the family than would be expected by chance.
Obviously, however, police forces seize a much higher number of cannabis plants: 507, 396 to the UK Border Agency's five.
The researchers suggest that by allowing tests on a much higher number of animals, steroid abuse could be reduced.
"We found a much higher number of fast-food outlets in more deprived areas where a higher number of black and minority ethnic populations resided.
In his statement today, Colonel Hla Min said that a much higher number of prisoners had been freed and that the releases would continue.
Similar(1)
About half of recent small quakes, he found, took place along postglacial faults--a much higher number than expected.
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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