# Finding the maximum/absolute error in calculating the density of a metal sample.

nerdy_hottie

## Homework Statement

"You are measuring the density of a metal sample. You have determined that the mass of the sample is 63.8 grams, and your error in this result is plus or minus 0.1 g. The volume of the sample is 8.8 +/- 0.1 cm^3. What is the maximum error (in g/cm^3) in your measurement of the sample density? "

## Homework Equations

density=mass/volume
For z = x/y:
δz/z = δx/x + δy/y

## The Attempt at a Solution

Well, filling into the equation for δz/z and substituting this for δρ/ρ and solving for δρ:
δρ=ρ(δm/m + δv/v)
=(63.8g/8.8cm^3)(0.1g/63.8g + 0.1cm^3/8.8cm^3)
=(7.25g/cm^3)(0.01293)
=0.0937g/cm^3

However, it says this answer is incorrect.
Any hints on where I am going wrong?

szynkasz
Maybe it should be done in this way:
$$\rho_{max}=\frac{m+\Delta m}{V-\Delta V}\\ \rho_{min}=\frac{m-\Delta m}{V+\Delta V}\\ \Delta\rho=max\left(\rho-\rho_{min},\rho_{max}-\rho\right)$$

Last edited:
nerdy_hottie
I'm not quite sure I understand that last equation..

szynkasz
You choose larger of these two differences.

nerdy_hottie
ok thanks for the clarification but that still doesn't produce the correct answer. Thanks for your help though.

szynkasz