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

Advertisements
Advertisements

PROBLEM:

A good-quality measuring tape can be off by 0.50 cm over a distance of 20 m. What is its percent uncertainty?


Advertisements
Advertisements

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%.


Advertisements
Advertisements