The mass of a box measured by a 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?
Given:
Mass of the box (m): 2.300 Kg (2 significant figures, 1 after decimal)
Gold pieces: G1 = 20.15 g = 0.02015 Kg (4 significant figures) and G2 = 20.17 g = 0.02017 Kg (4 significant figures)
(a) total mass of box (M) = m + G1 + G2
M = 2.300 + 0.02015 + 0.02017 = 2.34032 Kg but in addition the final result should have significant digits after decimal equal to the minimum number of significant digits of all the numbers used.
Therefore, M = 2.3 Kg (upto 2 significant digits and 1 after decimal due to 1 significant digit in m)
(b) difference in the masses = G2 – G1 = 0.02 g (1 significant digit). In subtraction the final result should have significant digits after decimal equal to the minimum number of significant digits of all the numbers used.
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