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The phrase "a far smaller number" is correct and usable in written English.
It can be used when comparing quantities to emphasize that one quantity is significantly less than another.
Example: "In the recent survey, a far smaller number of participants reported satisfaction with the service compared to last year."
Alternatives: "a significantly lower number" or "a much smaller amount".
Exact(45)
A far smaller number say they live for being at war and vow never to leave.
Heating-oil users (a far smaller number, concentrated in the north-east) should expect a 27% hike.
Most American officers and officials whom I spoke to expected a far smaller number — closer to fifteen thousand.
We desperately need changes in policy – our asylum laws were written a long time ago when there was a far smaller number of political refugees.
(Bosnian Muslims had killed several hundred Serb civilians around the enclave, a far smaller number than the seven thousand killed by Mladić's forces in 1995).
A far smaller number, about 100,000, actually go to a single Web site to view their incoming bills and electronically pay them, according to Gartner.
Similar(15)
A significant but far smaller number of respondents (28%%) found that lack of knowledge of alternatives or initiatives and suitably qualified manpower was an impediment.
The other 59 victims (13%) were internationals, which though a far smaller overall number illustrates a greater rate of attack when compared to their numbers in the field (it is estimated that less than 8% of humanitarian staff in the field are internationals) (ibid, p. 3).
But it has suffered a string of humiliating defeats by far smaller numbers of jihadist militants from Islamic State (IS) since January 2014.
Far smaller numbers blame a shortage of freeways, poor public transit, lax enforcement of traffic laws or bad drivers.
But he also mentioned some far smaller numbers that startled a soft-drink drinker.
More suggestions(16)
a far greater number
a far smaller reduction
a far smaller sum
a far smaller database
a far smaller fraction
a far smaller price
a far smaller following
a far smaller continent
a far smaller area
a far smaller talent
a far smaller figure
a far smaller haul
a far lower number
a far smaller kick
a far bigger number
a far smaller lobbying
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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