Degree of accuracy to express $T$? I conducted a pendulum experiment and here are my results:
10T / s:
( The time taken for 10 oscillations measured on a stopwatch that only shows the time to 2 decimal places. Measured in seconds )
For a 50 cm Pendulum. The time takes for 10 oscillations is 14.31 seconds.
I want to find T / s. The time taken for 1 oscillation using the result from above. I can do this by dividing by 10. However to how many significant figures or decimal places should I express the answer? If 10T is measured to 2 decimal places then should T also be measured to 2 decimal places, or should significant figures be used? Furthermore what if I wanted to express $T^2$. To what degree of accuracy would I express this and why.
Edit: Say I measured 14.31 seconds on a stopwatch which only displays values to 2 decimal places. I want to divide this value by 10. Would I express my answer as 1.431 (4sf) or 1.43 and why? Furthermore what if I wanted to square this answer ( Eg. Either 1.431 or 1.43 )? To what degree of accuracy should my answer be?
 A: Absolute error propagation in calculations is defined by :
$$ \Delta_f = \sum_n \left| \frac{\partial f(x_1,x_2,\ldots, x_n)} {~\partial x_n} \right| \cdot \Delta {x_n} \tag 1$$
Your function is $f=s\cdot t \tag 2$, where $s$ is time scaling constant, namely $s=\frac {1}{10}.$ Putting (2) into (1) gives:
$$ \begin{aligned}
\Delta_f &= \left| \frac{\partial (st)} {~\partial t} \right| \cdot \Delta 
{t} \\&= \left| s \frac{\partial t} {~\partial t} \right| \cdot \Delta 
{t} \\&= s \Delta t   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(3)
\end{aligned}
,$$
Where $\Delta t$ is stopwatch measurement error. Putting scaling constant and stopwatch error into (3), gives your division by 10 resulting error propagation :
$$ \Delta_f = 0.1 \times 0.01s = 0.001s \tag 4$$
So to say resulting error is in the third decimal digit,  thus you should format your resulting pendulum period to two decimal places like $T=1.43s$ or $T=1.43(1)s$. Insignificant digits here is marked with () parentheses.
Repeat above given error propagation calculation procedure for your another function case $f= s^2\cdot t^2.$
