Question: Multiplication of Matrices

This is a personal pet peeve. Let A be a 2x2 matrix with elements 0.5, 0.5, 0.3, 0.7 Find A^2 Repeat with a 2x2 matrix with elements 1/2, 1/2, 3/10, 7/10. Why does the first example give more than 2 decimals? Why is the answer to the first so inaccurate? Is there some library besides LinAlg or LinearAlgebra I should include to handle such rudimentary calcs?
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