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. $164\pm3~\text{cm}^2$
2. $163.62\pm2.6~\text{cm}^2$
3. $163.6\pm2.6~\text{cm}^2$
4. $163.62\pm3~\text{cm}^2$

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 cm² (By rounding off to one significant figure)
Therefore, area, A =A ±ΔA =(164±3) cm²
Hence, option (1) is the correct answer.

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