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Question

You measure two quantities as A = (1.0 ± 0.2) m and B = (2 ± 0.2) m then what should report correct value for AB is 


A
(1.41 ± 0.4) m
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B
(1.4 ± 0.15) m 
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C
(1.4 ± 0.3) m 
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D
(1.4 ± 0.2) m
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Solution

The correct option is C (1.4 ± 0.2) m
According to the problem A=1.0 m± 0.2 mB= 2.0 m ± 0.2 m Let Z=AB 

= (1.0)(2.0) = 1.414 mRoiunding of to two significants digits Z= 1.4 m
AB=1×2=1.414=1.4

Relaive error ΔZZ  = 12(ΔAA+ΔBB)=12×0.62,=0.15
ΔZZ=0.15 ,  ΔZ=0.210
Rounding off to one significant digit ΔZ= 0.2 m
the correct value for AB = (1.4 ± 0.2) m 
 

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