Significant Figures

The number of significant figures in any measurement indicates the degree of precision of that measurement. The following example illustrates the meaning of significant figures in a measurement.

Suppose we are required to measure the length of an object, say, a piece of chalk. We use a metre scale to measure its length and observe it to be 12.5 cm. We cannot measure this length to the second decimal place in centimetres because our measuring instrument, namely, the metre scale, can read up to an accuracy of only one-tenth of a centimetre.

This measurement is, therefore, not exact but only approximate.

How reliable this measurement is, can be easily checked by measuring the same length a couple of times. Most often (at least six times out of ten) the result is 12.5 cm, although once or twice the length may also turn out to be 12.4 cm or 12.6 cm. The variation of the digit after the decimal place is due to personal error inherent in any measurement. This means that in 12.5 cm, the figures 1 and 2 are absolutely correct, but the figure 5 is only reasonably correct.

We are not hundred percent certain about the correctness of the figure 5 but this figure 5 is as significant as the figures 1 and 2. We say that in the measurement of a length of 12.5 cm, there are three significant figures, namely, 1, 2 and 5. Significant figures give actual information about the magnitude of quantity.

The number of significant figures in any measurement indicates the degree of precision of that measurement. It is absurd to express the length to four significant figures as 12.53 cm using a metre scale. The figure 3 is not significant because it claims to give information, which cannot be obtained with a metre scale.

However it is perfectly legitimate to express the length as 12.53 cm, if it is measured with the help of Vernier Callipers, which can measure lengths up to an accuracy of one-hundredth of a centimeter. In such a measurement, four figures namely 1, 2, 5 and 3 are significant. This measurement, therefore, has a higher degree of precision.