# Use DE to show error percentage

1. Nov 4, 2013

1. The problem statement, all variables and given/known data
Use Differentials to show that an error of 2% in the measurement of the side of a square results in an error of approximately 4% in the calculation of the area

2. Relevant equations

I'm using Area =(sΔx)^2

3. The attempt at a solution
Using Δx=0.02,
Area= $s^{2}$$0.02^{2}$ =$s^{2}$/2500=0.04%$\times$$s^{2}$

2. Nov 4, 2013

### Staff: Mentor

This is incorrect. The formula for area is A = s2. The differential of the area would be dA = (dA/ds) * ds ≈ dA/ds * Δs.

Don't confuse yourself by using two variables for the length of a side of the square. You shouldn't have both s and Δx in your work.

3. Nov 4, 2013

### Ray Vickson

Do you really not know the difference between 4% and .04% ?

4. Nov 8, 2013