1.4 Use of Significant Figures

1.4 Use of Significant Figures

The number of digits of a measurement about which we do feel reasonably sure are called significant figures. In fact, they reflect the use of actual instrument used for that measurement.

While using a calculator, the result of any calculation contains many digits after the decimal point. The additional digits may mislead another person who uses those figures into believing them. Hence, they are to be rounded off to the correct number of significant figures. This can be done by keeping in view the uncertainty or the least count of the instrument while recording observations and also quoting results of any calculations to the correct numbers of significant figures.

It is better to quote the result in scientific notation to avoid any ambiguity regarding the number of significant figures.

For example, weighing the same object with different balances:

• Electronic balance: mass = $3.145 \pm 0.001\,\mathrm{g}$
• Lever balance: mass = $3.1 \pm 0.1\,\mathrm{g}$

Usually, the uncertainty $\pm 0.001\,\mathrm{g}$ or $\pm 0.1\,\mathrm{g}$ is dropped, and it is understood that the number quoted has an uncertainty of at least $1$ unit in the last digit. All digits which are quoted are called significant figures.

In any measurement, the accurately known digits and the first estimated or doubtful digit are called significant figures.

Proper use of significant figures ensures that we correctly represent the uncertainty of our measurements. For example, scientists immediately realize that the reported mass $3.145\,\mathrm{g}$ is more accurate than a reported mass of $3.1\,\mathrm{g}$, reflecting the use of a better or more precise instrument. As we improve the quality of our measuring instrument and techniques, we extend the result to more and more significant figures and correspondingly improve the experimental accuracy of the result.