Numerical analysis. You want to measure a length with a relative error of less than 0.5%. What is the minimalongitud that must be.

You want to measure a length with a relative error of less than 0.5%. What is the minimum length which should be able to appreciate the measuring instrument if the measure is 20 cm? And if they were 40 m?......

2voto

Anon User Points 0
The relative error is the quotient between the absolute error and the true value, which is the arithmetic mean of all measured values. To express in % we multiply by 100: 
\begin{align}&\epsilon_r=\frac{\epsilon_a}{V}·100\end{align}As the minimum absolute error that can be committed is the inaccuracies of the device (the minimum length that can be measured), if the true value is 20 cm, the inaccuracy will be


\begin{align}&\epsilon_a=\frac {\epsilon_r·V}{100}=\frac{0,5·20}{100}=0,1\ cm\end{align}If the true value is 40, the inaccuracy of the device will be


\begin{align}&\epsilon_a=\frac {\epsilon_r·V}{100}=\frac{0,5·40}{100}=0,2\ cm\end{align}

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