We should measure the side of a square to be sure of calculating the area to within 4% of its true value is upto 4 decimal places.
If the computed area has to be within 4% of the actual area, the absolute value of the area error, dA, has to be less than or equal to 0.04A.
Let x be the square's actual side length. Create an equation for AA and then calculate its derivative.
When dA = 4xdx and A = x2 are substituted into the equation,
4xdx = 0.04x 2 = 0.04x^ 2 = 0.0016x
When the equation for dx, which is the inaccuracy in the measurement of the side length, is solved.
Because 4x>0, it may be extracted from the absolute value and split to the opposite side.
The inaccuracy in measuring the side length x must then be less than 1%.
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