What is the maximum potential error in terms of percentage?

Question

A pharmacist attempts to weigh 120mg of codeine sulphate on a balance with a sensitivity requirement of 6mg. Calculate the maximum potential error in terms of percentage.

The answer is 5%. Please do show the solution. Thanks!

Answer 1

The sensitivity is $6$ mg, so the maximum weight given is $126$ mg.

the error is $126-120=6$ mg.

in percentage, it is

$$\frac {6}{120}\times 100=5 \%$$

Answer 2

If 120mg codeine sulphate is weighed the balalance show at maximum $120mg+6mg=126$

And the balance show at minimum $120mg-6mg=114$

And the relative error can be calculated with the minimum and the maximum

$$\frac{126mg-120mg}{120mg}=\frac{120mg-114mg}{120mg}=\frac{6mg}{120mg}=0.05=5\%$$