Tag Archives: uncertainty of a tape with an error

Problem 1-12: Solving for the percent uncertainty of a 20-m tape that is off by 0.50 cm

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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,

% uncertainty=δll×100%=0.5 cm20 m(100 cm1 m)×100%=0.5 cm2000 cm×100%=0.025 %  (Answer)\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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