Explain the statement: "The accuracy of a measurement cannot be determined by absolute error,but only by percentage error."
(N/A) Let us consider measuring the lengths of two different objects using the same Vernier calipers,yielding values of $2.20 \pm 0.01 \text{ cm}$ and $8.05 \pm 0.01 \text{ cm}$.
Here,the absolute error in each measurement is the same $(0.01 \text{ cm})$.
The percentage error in the first measurement is $\frac{0.01}{2.20} \times 100 \% = 0.45 \%$.
The percentage error in the second measurement is $\frac{0.01}{8.05} \times 100 \% = 0.12 \%$.
Thus,even though the absolute errors are identical,the percentage error is smaller for the larger measurement and larger for the smaller measurement. Therefore,it can be concluded that the smaller the percentage error,the more accurate the measurement is.
Here,the absolute error in each measurement is the same $(0.01 \text{ cm})$.
The percentage error in the first measurement is $\frac{0.01}{2.20} \times 100 \% = 0.45 \%$.
The percentage error in the second measurement is $\frac{0.01}{8.05} \times 100 \% = 0.12 \%$.
Thus,even though the absolute errors are identical,the percentage error is smaller for the larger measurement and larger for the smaller measurement. Therefore,it can be concluded that the smaller the percentage error,the more accurate the measurement is.
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