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0.00001 inch
That would also depend on the thickness of that square inch!
The thickness of a plastic ID card or credit card is approximately one millimeter, It is also the approximate thickness of a stack of 10 pieces of paper. One millimeter is approximately a sixteenth of an inch.
One fourth of 1 inch. Look at a ruler and divide a half inch in half-that's a quarter inch.
You could not have one. A square is a 2-dimensional shape and a 2-d shape has no thickness. No thickness means no mass and no mass means no weight. Simple!