Physics, like any other science, is based on observation and experiment. By performing an experiment we have to take measurements.
Accuracy is how close a measurement is to the correct value for that measurement.
The precision of the measurements refers to the spread of the measured values.The precision of the measurements would be to determine the range, or difference, between the lowest and the highest measured values.
For example let’s say what we want to measure a plain A4 paper’s dimensions, the most common paper standard in the world. We use our ruler and we write down three :
1st measure 20.9 x 29.5 cm, 2nd measure 21.2 x 29.9 cm, 3rd 21.1 x 29.8 cm.
Our lowest value was 20.9 x 29.5 and the highest value was 21.2 x 29.9 cm.
We can easily find that A4 paper size is 21.0 x 29.7 cm (or 210 x 297 mm or 0.21 x 0.297 m).
Our measument (A4 parer example) was both accurate and precise, but in some cases are accurate but not precise, or they are precise but not accurate.
Physical quantities obtained from experimental observation always have some uncertainity. Measurements can never be made with absolute precision.
The uncertainty in a measurement, A , is often denoted as δA (“delta A ”), so the measurement result would be recorded as A ± δA .
The error in the use of any instrument is normally taken to be half of the smallest division on the scale of the instrument. Such an error is called instrumental error. In the case of a metre scale, this error is about 0.5 mm.
The factors contributing to uncertainty in a measurement include:
a. Limitations of the measuring device,
b. The skill of the person making the measurement.
The digits which tell us the number of units we are reasonably sure of having counted in making a measurement are called significant figures.
For example, 1.435 cm has four significant figures. But in different units, the same can be written as 0.01435 m or 14.35 mm. All these numbers have the same four significant figures.
From the above example, we have the following rules:
i. All the non−zero digits in a number are significan,
ii. All the zeroes between two non−zeroes digits are significant, irrespective of the decimal point,
iii. The zeroes at the end without a decimal point are not significant.