Question

The length and breadth of a rectangular object are 25.2 cm and 16.8 cm respectively and have been measured to an accuracy of 0.1 cm. The relative error and percentage error in the area of the object are:

• A. 0.01 ; 1%
• B. 0.1 ; 10%
• C. 1 ; 10 %
• D. 1 ; 100 %

Answer 1

The correct option is A 0.01 ; 1%

$Area=l\times b$

$\frac{△A}{A}=\frac{△l}{l}+\frac{△b}{b}$

$=(\frac{0.1}{25.2}+\frac{0.1}{16.8})=0.00992\approx 0.01$

This is the relative error.
Percentage error $=0.01\times 100=1\%$