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The phrase "a far narrower margin" is correct and usable in written English.
It can be used when discussing a comparison that highlights a significantly smaller difference or allowance between two or more items, situations, or outcomes.
Example: "The latest poll results show that the candidates are competing with a far narrower margin than in previous elections."
Alternatives: "a much smaller margin" or "a significantly tighter margin".
Exact(3)
And some other Republicans — who now must contend with a far narrower margin of 17 Republicans to 16 Democrats in the State Senate — still sounded uncompromising.
Indiana voters trusted Hillary on the economy, but by a far narrower margin than previous primaries.
But asked which candidate's policies they most agreed with, respondents sided with her by a far narrower margin, giving her 44percenttoTrumpump's 40percentt.
Similar(57)
H.P. Shareholders Register Their Frustration | Shareholders of Hewlett-Packard re-elected the company's board members, but by far narrower margins than last year, Reuters reports.
That's a far narrower construction.
East by a somewhat narrower margin.
It also predicted a Tory win, but by a much narrower margin.
Most analysts expect that this election will be decided by a much narrower margin.
By a narrower margin -- 49percentto43percentcent -- those polled supported establishing a Palestinian state.
Flake won by a margin of about three percentage points, while Heller won by an even narrower margin.
John Kennedy's election was by a narrower margin in the popular vote than the 300,000 margin that currently exists here.
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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