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,

 length l=(16.2±0.1)cm Breadth b=(10.1±0.1)cm Area A=l×b=(16.2cm)×(10.1cm)=163.62cm2 

Rounding off to three significant digits, area A = 164 cm2

Step 2: Find the error.

ΔAA=Δll+Δbb=0.116.2+0.110.1=1.01+1.6216.2×10.1=2.63163.62
  ΔA = A ×2.63163.62=163.62×2.63163.62=2.63cm2
⇒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.