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The phrase 'approximately how long' is correct and usable in written English
You can use it when you need to estimate an amount or duration, such as a length of time. For example, you might say, "Can you give me an idea of approximately how long it will take to complete the project?"
Exact(12)
Approximately how long are ALZ medications (such as Aricept or any others) beneficial?
The G.P.S. tracker let me know approximately how long I could afford to sleep without missing his arrival in Nikolai.
Its longer-running battery lets you see a display that shows approximately how long the electrons will keep flowing.
What's nice is that Armstrong also breaks these down into approximately how long it will take an average person to read them.
So, whereas the frequency selectivity of the channel provides the information about which subcarriers along the entire transmission bandwidth are undergoing the best, the worst, and intermediate conditions, the fading rapidity indicates (i.e., depending on the carrier frequency and UE speed) approximately how long time the conditions over those subcarriers will be steady.
It is also possible to estimate how long ago two living clades diverged – i.e. approximately how long ago their last common ancestor must have lived – by assuming that DNA mutations accumulate at a constant rate.
Similar(47)
An assessment was made if the foetus was alive during parturition or dead in uterus, and if so, approximately for how long before expulsion.
When calling Poison Control, in addition to the name and telephone number, be prepared to report the following: What was swallowed, approximately how much and how long ago?
Blood samples were drawn from weeks 4 through 14 of pregnancy, and women were asked at approximately week 12 how long it had taken to conceive and whether the pregnancy was planned.
This question may be answered by asking whether food intake has been decreased up to the time of screening and if so by approximately how much and for how long.
How long has the service existed (approximately)?
More suggestions(2)
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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