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

Question

Infinity Learn · Accepted Answer

If △x is error in a physical quantity, then relative error is calculated as △xx  Given, lengthl $$=$$ (16.2$$ ±$$0.1) cmBreadth b $$=$$ (10.1$$± $$0.1) cmArea A $$=$$ l ×b $$=$$ $$16.2$$ × $$10.1$$ $$=$$ $$163.62cm2Rounding$$ off to three significant digits, area A $$=$$ $$164$$ $$cm2$$△$$AA=$$△$$ll+$$△bb $$=$$ $$0.116.2+0.110.1=$$ $$1.01+1.6216.2$$ ×$$10.1$$ $$=$$ $$2.63163.62$$⇒△$$A=163.62$$×$$2.63163.62$$ $$=$$ $$2.63$$ $$cm2$$△A $$=$$ $$3$$ $$cm2(By$$ rounding off to one significant $$figures)Area$$, A $$=$$ A△A $$=$$ (164$$±$$3) $$cm2$$

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

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