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estimation is to think of an answer before measuring the quantity and approximation is to round off.
Approximation: around, almost, approximation means estimation. You think the number is around the right answer example: 2258+3695= approximatly 6050 estimation= ST Mate
Yes.
There is no single word. Mathematical methods, alone, could involve analytical methods, statistical methods of estimation or numerical methods for approximation.
If an estimation, or estimate, is a guess, an approximate estimation is a rougher guess.