Question

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

Answer 1

Given, the mass of the box is 2.300 kg and the masses of the two gold pieces are 20.15 g and 20.17 g .

(a)

The significant figure for the mass of the box is 2 , and the significant figures for the two gold pieces are 4 and 4 respectively.

The total mass of the box after addition of two gold pieces is,

M=2.300 kg+20.15 g+20.17 g =2.300 kg+40.32 g× 10 −3  kg 1 g =2.34032

Since, the significant for the mass of the box is least, that is 2 , so the significant figure for the total mass of the box must be 2. Hence, the total mass of the box is 2.3 kg .

(b)

The differences in the masses of the two gold pieces are,

Δm=20.17 g−20.15 g =0.02 g

Since, the least number after the decimal point is 2 for the masses of the two gold pieces. So, the difference in the masses of the two pieces must contain two digits after the decimal point. Hence, the difference in the masses of the two gold pieces are 0.02 g .