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The phrase "an approximate rate of" is correct and usable in written English.
It can be used when discussing an estimated or rough figure related to a specific measurement or calculation.
Example: "The project is expected to have an approximate rate of 5% growth over the next year."
Alternatives: "an estimated rate of" or "a rough rate of".
Exact(38)
Each respirometer was supplied with water at an approximate rate of 3 L min−1 (total volume of the recirculating system was approximately 150 L).
In irradiated mice, body weight was significantly decreased starting day 14 with an approximate rate of −0.27 g/day and reached a nadir at day 22 with approximately 18.5% body-weight reduction.
The federal government provides matching funds for federal highway improvements at an approximate rate of 80 cents for every 20 cents collected by the state.
It was expected that approximately 667 patients would have to be screened in order to obtain 600 randomised patients, assuming an approximate rate of 10%% screening failures.
For TiO2-treated cells, the MMP level decreased continuously after the PDT with an approximate rate of 1.2% per min within 60 min.
Water is needed to retort or extract oil shale at an approximate rate of three volumes of water for every volume of oil produced.
Similar(22)
Analysis of the resulting kinetic data gave an approximate rate constant for the reaction of HOSCN with this compound of ~30 M−1·s−1 (Table 1).
SERT binding in 3 to 18 years old children and adolescents shows an increase [ 8], followed by a decrease at the approximate rate of 10percentt per decade [ 9].
He also introduced the measurement of nitrogen in the urine as an indication of the approximate rate of protein metabolism in the entire animal and was first to show that human digestive glands may be influenced by secretory nerves.
The approximate rate of live births using frozen eggs, based on those thawed in 2013, was 14%.
Automobiles with manual transmissions, not automatic, have been declining in the United States at the approximate rate of 1percentt a year.
More suggestions(16)
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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