Q 2.12: The mass of a box measured by a grocer’s balance is 2.30 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 difference in the masses of the pieces = 20.17 - 20.15 = 0.02 g (which has only one significant digit !)
Since two is the least number of decimal places, the total mass = 0.02 g.
The mass of the box = 2.30 kg
and the mass of the first gold piece = 20.15 g = 0.02015 kg
The mass of the second gold piece = 20.17 g = 0.02017 kg
(a) The total mass = 2.30 + 0.02015 + 0.02017 = 2.34032 kg
Since one is the least number of decimal places, the total mass = 2.3 kg.
(Note: For addition/subtraction, the number of places after the decimal point in the answer is less than or equal to the number of decimal places in every term in the sum; i.e decided by the numbers after the decimal.)