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The phrase "a far better approximation" is correct and usable in written English.
It can be used when comparing two or more estimates or representations, indicating that one is significantly more accurate than the others.
Example: "After analyzing the data, we found that our new model provides a far better approximation of the actual results than the previous one."
Alternatives: "a much more accurate estimate" or "a significantly improved approximation."
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Second, tests show that relative to a flat soffit, this curved soffit on a cork mat enables far better approximation to the reference CPD.
A far better approach would be to recognize the fact that a product or geographic market is at best an approximationnecessary to calculate some percentage figures.
A far better alternative exists.
"I am a far better fighter now.
That's a far better outcome.
Football today is a far better spectacle.
George W Bush was a far better speaker.
A far better approach?
A far better and free option?
Honesty is a far better policy.
In the atmosphere, however, the variation of ρ with z is far from negligible and (124) is unreliable as a consequence; a better approximation is given below in the section Hydrodynamics: Compressible flow in gases.
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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