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The length and breadth of a rectangular ...

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

A

`164+-3cm^(2)`

B

`163.62+-2.6 cm^(2)`

C

`163.6+-2.6 cm^(2)`

D

`163.62+-3 cm^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`"Given"," ""length "l=(16.2+-0.1)cm`
`" ""Breadth "b=(10.1+-0.1)cm`
`" ""Area "A=lxxb`
`" "=(16.2 cm)xx(10.1 cm)=163.62 cm^(2)`
Rounding off to three significant digits, area`A=164 cm^(2)`
`(DeltaA)/A=(Deltal)/l+(Deltab)/b=(0.1)/(16.2)+(0.1)/(10.1)`
`=(1.01+1.62)/(16.2xx10.1)=(2.63)/(163.62)`
`Rightarrow" "DeltaA=Axx(2.63)/(163.62)=163.62xx(2.63)/(163.62)=2.63 cm^(2)`
`" "DeltaA=3 cm^(2)" ""(by rounding off to one significant figure)"`
`therefore" ""Area",A=A+-DeltaA=(164+-3)cm^(2).`
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