What are significant figures? What are significant digits? Explain with examples.

(N/A) Every measurement involves errors. The result of a measurement should be reported in a way that indicates the precision of the measurement.
Normally,the reported result of a measurement is a number that includes all digits known reliably plus the first digit that is uncertain.
The reliable digits plus the first uncertain digit are known as significant digits or significant figures.
- The digits in a significant figure are called significant digits.
- In any significant figure,the last digit (the rightmost) is uncertain.
- For example,the periodic time of a simple pendulum is $1.62 \ s$. In this,$1$ and $6$ are reliable and certain,while the digit $2$ is uncertain. Thus,in this observation,there are $3$ significant digits.
- When the length of an object is reported as $287.5 \ cm$,in this measurement,$2, 8,$ and $7$ are certain,while the digit $5$ is uncertain.
- Reporting the result of a measurement that includes more digits than the significant digits is superfluous and misleading,as it would give a wrong idea about the precision of the measurement.
- $A$ change of units does not change the number of significant digits in a measurement.
- For example,in the measurement of length $2.308 \ cm$,there are $4$ significant digits. It can be represented as $0.02308 \ m$,$23.08 \ mm$,or $23080 \ \mu m$.
- In each case,the significant digits are $2, 3, 0, 8$; hence,there are $4$ significant digits.
- Thus,the location of the decimal point is of no consequence in determining the number of significant figures.