Question

A good-quality measuring tape can be off by 0.50 cmover a distance of20 m. What is its percent uncertainty?

Short answer

The Percent Uncertainty given case is ${\mathrm{\delta }}_{\mathrm{L}}=0.025\%$.

Step-by-step solution

Defining concept of percentage uncertainty

Percentage uncertainty is just 100 percent related uncertainty. Since percentage uncertainty is also a measure of the same value, it has no units.

Given Data

Consider the given data as below.

Original Length= $\mathrm{L}=20\mathrm{m}$

Uncertainty in Length, ${\mathrm{\delta }}_1=0.50\mathrm{cm}=0.50\times {10}^{-2}\mathrm{m}$

Defining percentage uncertainty formula

According to a mathematical formula,-

$$\begin{gathered} \mathrm{Percent}\mathrm{Uncertainty}=\frac{{\mathrm{\delta }}_1}{\mathrm{L}}\times 100\% \\ {\mathrm{\delta }}_{\mathrm{L}}=\frac{0.50\times {10}^{-2}\mathrm{m}}{20\mathrm{m}}\times 100\% \\ =0.025\% \end{gathered}$$

Stating conclusion

The Percent Uncertainty in the given case is ${\mathrm{\delta }}_{\mathrm{L}}=0.025\%$.