1.11 Significant Figures
We can count the number of candies in a jar and know it exactly by counting, but we cannot measure the height of the jar exactly. All measurements include uncertainties depending upon the refinement of the instrument which is used for measurement.
It is important to reflect the degree of uncertainty in a measurement by recording the observation in significant figures. The significant figures or digits are the digits of a measurement which are reliably known.
Consider a rod whose length is measured with a ruler. The measurement shows the length in between 4.6 cm and 4.7 cm. Since the length of the rod is slightly more than 4.6 cm but less than 4.7 cm, one student estimates it to be 4.6 cm while another student takes it as 4.7 cm. The first student thinks that the edge is nearer to the 6 mm mark, whereas the second student considers the edge of the rod nearer to the 7 mm mark. It is difficult to decide what the true length is.
Both students agree on the digit 4, but the next digit is doubtful, which has been determined by estimation only and has a probability of error. Therefore, it is known as a doubtful digit. In any measurement, the accurately known digits and the first doubtful digit are known as significant figures.