The uncertainties we have found so far are sometimes called absolute uncertainties, but percentage uncertainties are also very useful.
The percentage uncertainty expresses the absolute uncertainty as a fraction of the measured value and is found by dividing the uncertainty by the measured value and multiplying by $100\% $.

$percentage\,uncerta{\mathop{\rm int}} y = \frac{{uncerta{\mathop{\rm int}} y}}{{measured\,value}} \times 100\% $ 

For example, suppose a student times a single swing of a pendulum. The measured time is $1.4 s$ and the estimated uncertainty is $0.2 s$. Then we have:

$\begin{array}{l}
percentage\,uncerta{\mathop{\rm int}} y = \frac{{uncerta{\mathop{\rm int}} y}}{{measured\,value}} \times 100\% \\
 = \frac{{0.2}}{{1.4}} \times 100\% \\
 = 14\% 
\end{array}$

This gives a percentage uncertainty of 14%. We can show our measurement in two ways:
- with absolute uncertainty: time for a single swing $ = 1.4s \pm 0.2s$
- with percentage uncertainty: time for a single swing $ = 1.4s \pm 14\% $
(Note that the absolute uncertainty has a unit whereas the percentage uncertainty is a fraction, shown with a $\% $ sign.)
A percentage uncertainty of $14\% $ is very high. This could be reduced by measuring the time for 20 swings.
In doing so, the absolute uncertainty remains $0.2 s$ (it is the uncertainty in starting and stopping the stopwatch that is the important thing here, not the accuracy of the stopwatch itself), but the total time recorded might now be $28.4 s$.

$\begin{array}{l}
percentage\,uncerta{\mathop{\rm int}} y = \frac{{0.2}}{{28.4}} \times 100\% \\
 = 0.7\% 
\end{array}$

So measuring 20 oscillations rather than just one reduces the percentage uncertainty to less than $1\% $.
The time for one swing is now calculated by dividing the total time by 20, giving $1.42 s$. Note that, with a smaller uncertainty, we can give the result to two decimal places. The percentage uncertainty remains at $0.7\% $:

$time\,for\,a\,\sin gle\,swing\, = \,1.42s \pm 0.7\% $