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PROBLEM:
A good-quality measuring tape can be off by 0.50 cm over a distance of 20 m. What is its percent uncertainty?
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SOLUTION:
The percent uncertainty can be calculated by the uncertainty divided by the total measure, but the units should be the same. That is,
\begin{align*}
\%\:\text{uncertainty} & =\frac{\delta _l}{l}\times 100\% \\
\\
& =\frac{0.5\:\text{cm}}{20\:\text{m}\left(\frac{100\:\text{cm}}{1\:\text{m}}\right)}\times 100\% \\
\\
& =\frac{0.5\:\text{cm}}{2000\:\text{cm}}\times 100\% \\
\\
&=0.025\:\% \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)
\end{align*}Therefore, the percent uncertainty is 0.025%.
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