Ncert Exercises & Solutions

The length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm, respectively. The area of the sheet in appropriate significant figures and error would be, respectively,
1. 164 $\pm$ 3 ${cm}^{2}$
2. 163.62 $\pm$ 2.6 ${cm}^{2}$
3. 163.6 $\pm$ 2.6 ${cm}^{2}$
4. 163.62 $\pm$ 3 ${cm}^{2}$

(1) Hint: The result should have as many significant figures as there are in the value with the least significant figures.

Step 1: Find the area of the sheet.

Given,

$\begin{array}{l} length l = (16 .2 \pm 0 .1) cm \\ Breadth b = (10 .1 \pm 0 .1) cm \\ Area A = l \times b \\ = (16 .2 cm) \times (10 .1 cm) = 163 .62 {cm}^{2} \end{array}$

Rounding off to three significant digits, area A = 164 ${cm}^{2}$

Step 2: Find the error.

$\begin{array}{l} \frac{ΔA}{A} = \frac{Δl}{l} + \frac{Δb}{b} = \frac{0 .1}{16 .2} + \frac{0 .1}{10 .1} \\ = \frac{1 .01 + 1 .62}{16 .2 \times 10 .1} = \frac{2 .63}{163 .62} \end{array}$
$\begin{array}{l} \Rightarrow \end{array}$ $ΔA$ $=$ $A$ $\times \frac{2 .63}{163 .62} = 163 .62 \times \frac{2 .63}{163 .62} = 2 .63 {cm}^{2}$ $ΔA$ $=$ $3$ ${cm}^{2} (By rounding off to one significant figure) Area, A$ $=$ $A$ $\pm$ $ΔA$ $=$ $(164$ $\pm$ $3) {cm}^{2}$

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