Answer: The relative error of the resulting quantity is 0.018.
Explanation: Relative error of the quantities when are multiplied together is usually less than or equal to the sum of each relative error. Mathematically, it is represented as
[tex]\delta x=\frac{\Delta x}{x}[/tex]
According to the question,
Let us assume that the three quantities are [tex]r_1,r_2\text{ and }r_3[/tex]
[tex]r=r_1\times r_2\times r_3[/tex]
Taking log on both the sides, we get
[tex]log(r)=log(r_1\times r_2\times r_3)[/tex]
[tex]log(r)=log(r_1)+log(r_2)+log(r_3)[/tex]
Relative error is calculated by:
[tex]\frac{\delta r}{r}=\frac{\delta r_1}{r_1}+\frac{\delta r_2}{r_2}+\frac{\delta r_3}{r_3}[/tex]
[tex]\frac{\delta r}{r}=0.009+0.006+0.003=0.018[/tex]
This value has 3 significant figures only, so the resulting relative error is 0.018.
