### Question 2.12

NCERT Class XI Physics

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

### Solution

During addition and subtraction decimal places have to be taken into account - NOT the significant figures!$\displaystyle $

$ \begin{aligned} &\text{mass of box } m_b = 2.30 \equiv 2.3 \text{ kg} \\ &\text{it has } \textcolor{red}{\underline{1}} \text{ decimal digits}\\\\ &\text{mass } m_1 = 20.15 \text{ g} \equiv 0.02015 \text{ kg} \\ &\text{it has } \textcolor{red}{\underline{5}} \text{ decimal digits}\\\\ &\text{mass } m_2 = 20.17 \text{ g} \equiv 0.02017 \text{ kg} \\ &\text{it has } \textcolor{red}{\underline{5}} \text{ decimal digits}\\\\ &\text{add }2.3 + 0.02015 + 0.02017 = 2.3402\\ &\text{decimal digits to be min(1, 5, 5) = 1}\\\\ &\text{hence round to 1 place} = 2.3 \text{ kg}\:\underline{Ans}\\\\ &\text{(b) difference } 20.17 - 20.15 = 0.02\\\\ &\text{decimal places to be 2}\\\\ &\therefore 0.02 \text{ gm}\:\underline{Ans} \end{aligned} $

### Video Explanation

Please watch the following youtube video for a quick explanation:

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