The-side-of-a-square-is-measured-to-be-12cm-long-cofrect-to-the-nearest-cm-Find-the-maximum-absolute-error-and-the-maximum-percentage-error-for-a-The-length-of-the-square-Answer-0-5cm-

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Question Number 71696 by TawaTawa last updated on 18/Oct/19

$$\mathrm{The}\mathrm{side}\mathrm{of}\mathrm{a}\mathrm{square}\mathrm{is}\mathrm{measured}\mathrm{to}\mathrm{be}12\mathrm{cm}\mathrm{long}\mathrm{cofrect}$$$$\mathrm{to}\mathrm{the}\mathrm{nearest}\mathrm{cm}.\mathrm{Find}\mathrm{the}\mathrm{maximum}\mathrm{absolute}\mathrm{error}$$$$\mathrm{and}\mathrm{the}\mathrm{maximum}\mathrm{percentage}\mathrm{error}\mathrm{for}$$$$\left(\mathrm{a}\right)\mathrm{The}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{square}(\mathrm{Answer}:0.5\mathrm{cm},4.17\mathrm{\%})$$$$\left(\mathrm{b}\right)\mathrm{The}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{square}.(\mathrm{Answer}:12.25\mathrm{cm},8.5\mathrm{\%})$$

Answered by MJS last updated on 19/Oct/19

$$“\mathrm{to}\mathrm{the}\mathrm{nearest}{\mathrm{cm}}^{″}\mathrm{means}\pm .5\mathrm{cm}\mathrm{because}$$$$\mathrm{you}\mathrm{will}\mathrm{round}11.5\approx 12.0\mathrm{and}12.4\stackrel{.}{9}\approx 12.0$$$$\Rightarrow \mathrm{absolute}\mathrm{error}\mathrm{of}\mathrm{length}\mathrm{is}\pm .5\mathrm{cm}$$$$\Rightarrow \mathrm{percentage}\mathrm{is}\frac{.5}{12}\approx 4.17\mathrm{\%}$$$$11.5⩽x⩽12.5\iff 132.25⩽x⩽156.25$$$$x=12\pm .5\iff x^2={144}_{-11.75}^{+12.25}$$$$\Rightarrow \mathrm{absolute}\mathrm{error}\mathrm{of}\mathrm{area}\mathrm{is}12.25$$$$\Rightarrow \mathrm{percentage}\mathrm{is}\frac{12.25}{144}\approx 8.51\mathrm{\%}$$

Commented by TawaTawa last updated on 19/Oct/19

$$\mathrm{I}\mathrm{appreciate}\mathrm{your}\mathrm{time}\mathrm{sir}.\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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