Question

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 is

• A. $164 \pm 3 \mathrm {~cm} ^ { 2 }$
• B. $163.62 \pm 2.6 \mathrm {~cm} ^ { 2 }$
• C. $163.6 \pm 2.6 \mathrm {~cm} ^ { 2 }$
• D. $163.62 \pm 3 \mathrm {~cm} ^ { 2 }$

Answer 1

Answer: (A)

$164 \pm 3 \mathrm {~cm} ^ { 2 }$

Answer 2

Let length and breadth of a rectangular sheet are measured by a measured by using a meter scale as 16.2 cm and $10.1$ cm respectively. Each measurement has three significant figures.

$\therefore$Length l can be written as

L = $16.2 \pm 0.1 \mathrm {~cm} - 16.2 \mathrm {~cm} \pm 0.6 \%$

Similarly, the breadth b can be written as

$\mathrm { b } = 10.1 \pm 0.1 \mathrm {~cm} = 10.1 \mathrm {~cm} \pm 1 \%$

Area of the sheet,

$\mathrm { A } = 1 \times \mathrm { b } = 163.62 \mathrm {~cm} ^ { 2 } \pm 1.6 \%$

$= 163.62 \pm 2.6 \mathrm {~cm} ^ { 2 }$

Therefore, as per rule, area will have only three significant figures and error will have only one significant figure. Rounding off, we get $A = 164 \pm 3 \mathrm {~cm} ^ { 2 }$