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The phrase "improved by approximately" is correct and usable in written English
You can use it to describe a situation where someone or something has improved to some extent, but without knowing the exact amount of improvement. For example: "After adding a few new practices to their routine, his grade in math improved by approximately 20%."
Exact(57)
The safety per bicyclist was still improved by approximately 20%.
For poor flow however, performance was only improved by approximately 2%.
High temperature oxidation resistance is improved by approximately 40 times as compared to the untreated sample.
Interestingly, fracture toughness improved by approximately 30% when mixtures of microparticles and nanoparticles were used.
In addition to that, the corrosion resistance of steel substrate has been improved by approximately 30%.
With some slight opening on the base plate, the thermal resistance can be improved by approximately 12%.
The oxidation resistance of the coated specimens was improved by approximately twice as compared to the uncoated specimen.
The fracture toughness of the composites is improved by approximately 64% with the addition of co-carbon fillers.
Similar(3)
In all three cases the oxygen evolution overpotential at 1 A cm−2 which amounts under standard conditions to approximately 350 mV improves by approximately 80 100 mV.
In particular, the stored energy improves by approximately 43% compared with a rectangular cross section coil employing the same HTS tape length.
Results show that the overall performance improves by approximately 6.76% and 17.33% with a reduction in net unit weight by approximately 27.58% and 6.82% on changing the aspect ratio from 1.0 to 0.1 in case-I and case-II, respectively.
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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