The measurement of the side of a square floor tile is $7$ inches, with a possible error of $\frac{1}{32}$ inch.

$($a$)$ Use differentials to find the possible propagated error $($in square inches$)$ in computing the area of the square.

$+-,i{n}^2$

$($b$)$ Approximate the percent error in computing the area of the square. $($Round your answer to three decimal places.$)$

$\%$