precision
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significant figures . . . eh?
The term is precision.
360 degrees equals 2(pi) radians. Therefore, [2(pi)](623/360) = (623/180)(pi). Since I have not discovered any common integral factor for 623 and 180, I believe this is the simplest manner in which the exact radians measure can be written.
A degree in temperatire is a measurement of how hot or cold it is. A degree in education is the completion of a program, such as a bechelor's degree in education.
A degree can be a measurement of temperature, or part of the 360 degrees around a circle. A kilometre is a linear measurement of distance.