Aids to Understanding
Suppose you measure a piece of paper with the ruler below and you estimate it is a bit more than twenty two centimeters, say one fifth more.
The correct way to write your value is; 22.2 cm. Since the smallest scale division of the ruler is 0.5 cm the scale reading uncertainty is 0.25 cm , but we should
round it up (we never round uncertainties down) to 0.3 cm. The reading with uncertainty is written as
(22.2 +/- 0.3) cm. In meters we would write it as (0.222 +/- 0.003) m. It should now be clear that a ruler with 1.0 cm divisions we are justified in taking our reading to three decimal places. Excercise Suppose a ball is dropped from a height of 3.3000 m five times. Suppose the times on the digital stopwatch were, 0.81 s, 0.92 s, 0.79 s 0.95 s and 0.99 s.
Your job is to write a report identical to the one on the right and find the average speed with its absolute uncertainty.