Students A, B and C measure the length of a r | vedclass

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(A) The relative error is defined as the ratio of the absolute error (least count) to the measured value.For student $A$:Measured length $L = 9.5 \,m

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Student $A$

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(A) The relative error is defined as the ratio of the absolute error (least count) to the measured value.For student $A$:Measured length $L = 9.5 \,m = 950 \,cm$.Least count $\Delta L_A = 0.5 \,cm$.Relative error $RE_A = \frac{\Delta L_A}{L} = \frac{0.5}{950} \approx 0.000526$.For student $B$:Measured length $L = 9.5 \,m = 950 \,cm$. Since a meter scale $(100 \,cm)$ is used,the measurement is repeated $9.5$ times (effectively $10$ readings).Total absolute error $\Delta L_B = 10 	imes 0.1 \,cm = 1.0 \,cm$.Relative error $RE_B = \frac{1.0}{950} \approx 0.00105$.For student $C$:Measured length $L = 9.5 \,m = 950 \,cm$. $A$ foot scale is approximately $30.48 \,cm$. Number of readings $n = \frac{950}{30.48} \approx 31.17 \approx 32$ readings.Total absolute error $\Delta L_C = 32 	imes 0.05 \,cm = 1.6 \,cm$.Relative error $RE_C = \frac{1.6}{950} \approx 0.00168$.Comparing the relative errors,$RE_A < RE_B < RE_C$. Therefore,student $A$ reports the lowest relative error.

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