Order of magnitude

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"Order of" is often meant as "it's probably more or less right / at most a small factor off"

no technical definition
but conventionally maybe a factor 3-ish at most


"Order of magnitude"

when used more formally: a factor ten
when you know it's an estimation, you can read this as 'the decimal ought to be in the right place / probably has the right amount of zeroes on it'
when used less formally, see 'order of'


Ballpark figure is fuzzier.

It seems most people use it to mean something inbetween the above two, but not always.
The original meaning seems to be sports commentators eyeballing the amount of visitors based on filled and empty seats(verify) -- which would easily be better, within a few dozen percent
but for wider tasks, assume it is fuzzier. It depends on the task


https://en.wikipedia.org/wiki/Order_of_magnitude