Question

It has been found that the mass of a box measured by a grocer's balance is $2.300kg$. Two gold pieces of masses $20.15g$ and \[20.17g\] are added to the box.
(a) Calculate the total mass of the box?
(b) What will be the difference in the masses of the pieces to correct significant figures?

Answer 1

Hint: First of all find the number of significant figures in the parameters given in the question. Take their sum for the total mass. The number of significant figures in the total sum will be equivalent to the term with least number of significant figures. Then find the difference between the masses and compare their number of significant figures. This all will help you in answering this question.

Complete step by step answer:
The mass of the grocer’s box is given as,
\[{{m}_{b}}=2.300kg\]
This is having two significant figures.
The mass of the gold pieces are mentioned as,
\[{{m}_{1}}=20.15g=0.02015kg\]
This is having four significant figures.
\[{{m}_{2}}=20.175g=0.02017kg\]
(a) Adding up all the masses for the total mass can be written as,
\[M=\sum{m=2.3+0.02015+0.02017=2.34032kg}\]
As we can see, the initial mass has the least number of significant figures. That is two. Therefore, the final mass should not have more than two significant figures.
Therefore the total mass can be written as,
\[M=2.3kg\]
(b) When we subtract the mass of the gold pieces, we can write that,
\[d={{m}_{2}}-{{m}_{1}}\]
Substituting the values in it will give,
\[d=0.02017-0.02015=0.02g\]
As the initial mass is having four significant figures, the resulting difference will also have four or less significant figures in it. Therefore the number of significant figures in the resulting difference will be two in number. Hence the question has been answered.

Note:The significant figures of a number are the notations of their positions by which the digits are specified that are making a meaningful contribution to its measurement resolution. This is included in all the digits except the leading zeros. All other non-zero numbers are significant figures.