How does multiplying several measurements affect precision?
Answers
Assume you have a box or room of dimensions x, y and z with volume V.
The nominal volume is V = xyz. However, each of the linear measurements can be imprecise. Assume you may have errors in x, y and z of dx, dy and dz. Given these possible errors in the linear dimensions you can calculate the error in the volume.
Assume you have a box or room of dimensions x, y and z with volume V.
The nominal volume is V = xyz. However, each of the linear measurements can be imprecise. Assume you may have errors in x, y and z of dx, dy and dz. Given these possible errors in the linear dimensions you can calculate the error in the volume.
dV = (xy)dz +(xz)dy + (yz)dx.
Thus each error in a linear dimension is amplified by the product of the other two dimensions.