1.10 Uncertainty in a Measurement
There is no such thing as a perfect measurement. Whenever a physical quantity is measured (except counting), there is inevitably some uncertainty about its determined value due to the instrument used. This uncertainty may be due to a number of reasons. One reason is the type of instrument being used. Every measuring instrument is calibrated to a certain smallest division, and this fact puts a limit to the degree of accuracy which can be achieved while measuring with it.
Suppose we want to measure the length of a straight line with the help of a metre rule calibrated in millimetres. Let the end point of the line lie between 10.3 cm and 10.4 cm marks. By convention, if the end of the line does not touch or cross the midpoint of the smallest division, the reading is confined to the previous division. If the end of the line seems to be touching or has crossed the midpoint, the reading is extended to the next division. Thus, in this example, the maximum uncertainty is ±0.05 cm. It is equivalent to an uncertainty of 0.1 cm, equal to the least count of the instrument divided into two parts — half above and half below the recorded reading.
The uncertainty in small lengths, such as the diameter of a wire, or short intervals of time can be reduced further by taking multiple readings and then finding the average value. For example, the average time of one oscillation of a simple pendulum is usually found by measuring the time for thirty oscillations.
The uncertainty or accuracy in the value of a measured quantity can be indicated conveniently by using significant figures.