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The phrase "distance about" is correct and can be used in written English.
It means the approximate distance or the distance around something. Example: "The distance about the track was three miles." This means that the track was approximately three miles in total length.
Exact(60)
This transition occurs at a distance about halfway between Saturn's cloud tops and its centre.
He was in Allende's Chile when other writers fretted, at a distance, about it.
The museum is within walking distance (about three blocks) of the station.
There's no postmodern distance about them, no we-know-better-now wink.
It is walking distance (about five blocks) from the Shattuck Hotel, and longer walking distance from Stern Hall lodging.
He had certain frailties, he had an intellectual distance about him, and under pressure he could sometimes panic.
The thickly forested hills of CAR are visible in the distance, about two hours away by boat.
How can one possibly get critical distance about your subject when such moments are part of your experience of him?
Water can be heard gushing in the distance, about as close as I'm likely to get to the reservoir story.
The distance, about a mile and a half from the Rio Grande, was geographically negligible but enormously consequential.
It is shown that the characteristic two-peak line profile with the sharp edges arises at a large distance (about r ≈ (3 10) rg).
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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