# Math Help - Side of a square is 12 inches with a possible error of 1/64th of an inch?

1. ## Side of a square is 12 inches with a possible error of 1/64th of an inch?

1. Use differentials to approximate the possible propagated error in computing the area of the square.

2. Find the percent error to the nearest 100th of a percent.

I think I got the first one, A' = 3/8th in^2 but I have no idea how to get the second?

2. ## Re: Side of a square is 12 inches with a possible error of 1/64th of an inch?

The area of a square of side length x is, of course, $A= x^2$. The differential is $dA= 2x dx$ so if x= 12 inches and dx= 1/64 inch, $dA= 2(12)(1/64)= 3/8$ square inch as you say.

The "relative error" would be $\frac{dA}{A}$ and the "percent error" is that converted to a percent.