The total mass of a box measured by grocer's balance is $2.300 k g$ . Two gold pieces of masses $20.15 g$ and $20.17 g$ 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?

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Solution

$m_{i} = 2.300 k g$ ( $2$ significant digits)
$m_{1} = 20.15 g = 0.02015 k g$ ( $4$ significant digits)
$m_{2} = 20.175 g = 0.02017 k g$ ( $4$ significant digits)
(a)
Adding
$M = Σ m = 2.3 + 0.02015 + 0.02017 k g = 2.34032 k g$
But since the initial mass has least 2 signifincant digits, the final mass should not have more than 2 significant digits
Hence,
$M = 2.3 K g$
(b)
Subtracting
$m_{2} - m_{1} = 0.02 g$
Since the initial mass has $4$ significant digits, the result can have $4$ or less significant digits
Hence here the no. of significant digit $= 2$

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The total mass of a box measured by grocer's balance is 2.300 kg. Two gold pieces of masses 20.15 g and 20.17 g 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?

The total mass of a box measured by grocer's balance is $2.300 k g$ . Two gold pieces of masses $20.15 g$ and $20.17 g$ 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?