A person measures two quantities as A $$=$$ $$1.0$$ m ± $$0.2$$ m, B $$=$$ $$2.0$$ m ± $$0.2$$ m. We should report correct value for AB as

Question

A person measures two quantities as A $$=$$ $$1.0$$ m ± $$0.2$$ m, B $$=$$ $$2.0$$ m ± $$0.2$$ m. We should report correct value for AB as

Infinity Learn · Accepted Answer

Given, A $$=$$ $$1.0$$ m ± $$0.2$$ m, B $$=$$ $$2.0$$ m ± $$0.2$$ mLet, Y $$=$$ AB  $$=$$ (1.0)(2.0)   $$=$$  $$1.414$$ m∆YY $$=$$ $$12$$[∆$$AA+$$∆BB]$$=$$ $$12$$[$$0.21.0+0.22.0$$]  $$=$$  $$0.62$$×$$2.0$$⇒∆Y $$=$$ $$0.6$$ $$Y2$$×$$2.0$$ $$=$$ $$0.6$$×$$1.42$$×$$2.0$$ $$=$$ $$0.21Rounding$$ off to one significant digit∆Y $$=$$ $$0.2$$ mThus, correct value forAB  $$=$$ $$r+$$∆r $$=$$ $$1.4$$ ± $$0.2$$ m

A person measures two quantities as $A = 1.0 m \pm 0.2 m, B = 2.0 m \pm 0.2 m . We should report correct value for \sqrt{AB} as$

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A person measures two quantities as A = 1.0 m ± 0.2 m, B = 2.0 m ± 0.2 m. We should report correct value for AB as

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A person measures two quantities as $A = 1.0 m \pm 0.2 m, B = 2.0 m \pm 0.2 m . We should report correct value for \sqrt{AB} as$