Explain uncertainty or error in a given measurement with a suitable example.

(N/A) $(1)$ The length and breadth of a thin rectangular plate are $l = 16.2 \text{ cm}$ and $b = 10.1 \text{ cm}$. The least count of the meter scale is $0.1 \text{ cm}$,hence the absolute error in measurement is $0.1 \text{ cm}$.
$l = (16.2 \pm 0.1) \text{ cm}$
$b = (10.1 \pm 0.1) \text{ cm}$
Percentage error in measurement of length:
$\frac{0.1}{16.2} \times 100 \approx 0.6 \%$
$l = (16.2 \pm 0.6 \%) \text{ cm}$
Percentage error in measurement of breadth:
$\frac{0.1}{10.1} \times 100 \approx 1 \%$
$b = (10.1 \pm 1 \%) \text{ cm}$
Area of the rectangular plate:
$A = l \times b = 16.2 \times 10.1 = 163.62 \text{ cm}^2$
Percentage error in $A$:
$\frac{\Delta A}{A} \times 100 = \frac{\Delta l}{l} \times 100 + \frac{\Delta b}{b} \times 100 = 0.6 \% + 1 \% = 1.6 \%$
$\Delta A = \frac{1.6 \times 163.62}{100} \approx 2.6 \text{ cm}^2$
Area: $A = (163.62 \pm 2.6) \text{ cm}^2$
Since the minimum significant digits are $3$,the area should be represented as $A \approx (164 \pm 3) \text{ cm}^2$.
$(2)$ If a set of experimental data is specified to $n$ significant figures,a result obtained by combining the data will generally be valid to $n$ significant figures. However,if data is subtracted,the number of significant figures can be reduced. For example,$12.9 \text{ g} - 7.06 \text{ g} = 5.84 \text{ g}$. In subtraction,we consider the decimal places. Since $12.9$ has one decimal place,the result should be rounded to $5.8 \text{ g}$.