Question

The total mass of a box measured by grocer's balance is $2.300kg$. Two gold pieces of masses $20.15g$ and $20.17g$ are added to the box. What is:(a) the total mass of the box?(b) the difference in the masses of the pieces to correct significant figures?

Answer 1

$m_i=2.300kg$ ( $2$ significant digits)
$m_1=20.15g=0.02015kg$ ( $4$ significant digits)
$m_2=20.175g=0.02017kg$ ( $4$ significant digits)
(a)

Adding
$M=\Sigma m=2.3+0.02015+0.02017kg=2.34032kg$
But since the initial mass has least 2 signifincant digits, the final mass should not have more than 2 significant digits
Hence,
$M=2.3Kg$

(b)

Subtracting
$m_2-m_1=0.02g$
Since the initial mass has $4$ significant digits, the result can have $4$ or less significant digits
Hence here the no. of significant digit $=2$