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The phrase "a far smaller dose" is correct and usable in written English.
It can be used when comparing quantities, particularly in contexts related to medicine, substances, or measurements.
Example: "The new medication requires a far smaller dose than the previous one to achieve the same effect."
Alternatives: "a significantly lower dose" or "a much reduced dose".
Exact(2)
A new vaccine against bird flu developed by GlaxoSmithKline is more effective than any previous version and works at a far smaller dose, the company reported yesterday on its Web site.
In his deposition, the doctor, John Doe I, defended the use of less than five grams, emphasizing that nearly all people would be fully anesthetized at a far smaller dose and that most other states use only two grams.
Similar(58)
This is the same illumination that radiates in far smaller doses from smartphone and computer screens, to which we're advised to avoid exposure for at least an hour before bed, because it can suppress the production of melatonin.
Medically and chemically, there is very little difference between these drugs and illegal opiates such as heroin, and in some ways prescription synthetic opioids are worse, because they are fatal in far smaller doses.
71 72 However, far smaller doses are used intraocularly, and little reaches the systemic circulation.
A far smaller proportion is recycled.
Mere instinct suggests a far smaller number.
Strikingly, a far smaller proportion of B6.
Another possibility, more threatening to the public, is that Ms. Nguyen was somehow infected by spores from a tainted envelope, but with a dose far smaller than the minimum generally thought to be needed for infection.
These problems prompted a host of warnings and stimulated research that resulted in safer products containing far smaller hormone doses, less than one-hundredth the amount of estrogen in the original pill.
Something like Persil small & mighty laundry detergent gives great cleaning power in a much smaller dose.
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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