A recantangular metal slab of mass `33.333` has its length `8.0cm`, breath `5.0cm` and thickness `1mm`. The mass is measured with accuracy up to `1mg` with a senstive balance. The length and breath are measured with vernier calipers having a least count of `0.01cm`. The thickness is measured with a new a screw gauge of least count `0.01mm`. The percentage accuracy in density calculated from the above measurements is

Explanation

The percentage error itself gives us the percentage accuracy.
`d=(mass(M))/("length"(l) xx" breadth"(b) xx ("height"(h))=(M)/(lbh)`
`:.` The relative error is given by
`(Deltad)/(d)=((DeltaM)/(M))+((Deltal)/(l))+((Deltab)/(b))+((Deltah)/(h))`
Given l=8.0cm and `Deltal=0.01cm`
b=5.0cm and `Deltab=0.01cm`
h=1mm and `Deltah=0.01mm` and
M=33.333g and `DeltaM=1mg=0.001g`
Hence,`(DeltaM)/(M)=(0.001)/(33.333)`
`(Deltal)/(l)=(0.01)/(8.0),(Deltab)/(b)=(0.01)/(5)` and `(Deltah)/(h)=(0.01)/(1)`
The percentage error is given by,
`((DeltaM)/(m)+(Deltal)/(l)+(Deltab)/(b)+(Deltah)/(h)) xx 100`
`=((0.001)/(33.333)+(0.01)/8.0+(0.01)/(5)+(0.01)/(1)) xx 100`
`=0.003+0.125+0.2+1.0=1.328=1.3`
The percentage error is 1.3%