Question

The length and breadth of a rectangular sheet are $16.2cm$ and $10.1cm$, respectively. The area of the sheet in appropriate significant figures and error is

• A.
  $163.62\pm 3^{}c{m}^2$
• B.
  $164\pm 3^{}c{m}^2$
• C.
  $163.62\pm {2.6}^{}c{m}^2$
• D.
  $163.6\pm {2.6}^{}c{m}^2$

Answer 1

The correct option is B

$164\pm 3^{}c{m}^2$
Given, length of the sheet, $l=16.2cm$
And breadth of the sheet, $b=10.1cm$
So, area of the sheet, $A=\text{lb}$
$A=\left(16.2\right)\left(10.1\right)$
$A=163.62cm$
In multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures.
Here, the least significant figures are $3$.
As area is multiplication of length and breadth. So, area should be reported to three significant figures.
Therefore, rounding off the area, $A=164c{m}^2$
Absolute error in length, $\Delta l=0.1$
Absolute error in breadth, $\Delta b=0.1$
Let error in area be $\Delta A$
Then, relative error in area is,
$\frac{\Delta A}{A}=\frac{\Delta l}{l}=\frac{\Delta b}{b}$
$\frac{\Delta A}{A}=\frac{0.1}{16.2}+\frac{0.1}{10.1}=\frac{2.63}{163.62}$
Absolute error in area,
$\Delta A=2.63$
Rounding off, $\Delta A=3c{m}^2$