question_answer

Which of the following measurements is most accurate and which is most precise : (i)  4.00mm      (ii) 4.00 cm    (iii) 4.00 m       (iv) 40.00 m?

Answer:

                                                 

Length\[(l)\]	Least Count \[(\Delta l)\]	Relative Error \[(\Delta l/l)\]
(i) \[~\text{4}.00\text{ mm}\]	\[0.0\text{1mm}\]	\[\text{2}.\text{5}\times \text{ 1}{{0}^{\text{-3}}}\]
(ii) \[\text{4}.00\text{ cm}\]	\[0.0\text{1 cm}\]	\[2.5\times {{10}^{-3}}\]
(iii) \[\text{4}.00\text{ m}\]	\[0.0\text{1 m}\]	\[2.5\times {{10}^{-3}}\]
(iv) \[~\text{4}0.00\text{ m}\]	\[0.01\text{m}\]	\[2.5\times {{10}^{-4}}\]

Since the relative error in the measurement of 40.00 m is minimum, so this measurement is most accurate. The measurement 4.00 mm is most precise because it is measured with an instrument of minimum least count.