I am really very annoyed by how there are multiple perspectives about how we treat uncertainty in measurements and I want to get rid of the misconceptions once and for all.
I was finding the value of 'g'(acceleration due to gravity) using Kater's pendulum.
I measured the time taken for 100 oscillations of the pendulum with a stopwatch of least count 0.01 seconds, let's call it $t_1$ I obtained the time period of the pendulum by the relation, $T_1=t_1/100$
While finding the relative error in g I have to know the mean absolute error in $T_1$ Professor says that $\delta T_1=\delta t_1/100=0.0001 \: \rm s$
My argument, $\delta T_1=0.01 \: \rm s$ since the measurement is done only for 100 oscillations and you can't really consider the error in 100 oscillations as 100 times the error in 1 because if I were to take one oscillation I would never get such small error because of the low precision of stopwatch.
Professor says that taking 100 oscillations enables us to have a smaller error in the result.
But I feel this is wrong somehow
Even if we consider an ideal situation where the only error in measurement is due to the least count of the stopwatch, should you be able to measure a value of much higher accuracy than that enabled by the precision of the instrument?