Basic Mathematics and Measurements
7.0 Significant Figures
7.1 Rules to determine the significant figures
7.2 Rules for arthimetic operation with significant figures
7.0 Significant Figures
7.2 Rules for arthimetic operation with significant figures
The reliable digits plus the first uncertain digits are known as significant digits or significant figures.
Let us understand significant figure better with the help of an illustration.
Illustration: Measure the length of an object.
If one end of the object coincides with the zero of the metre scale, the other end may fall between $10.4\ cm$ and $10.5 \ cm$ mark of the scale.
The clear reading is $10.4\ cm$. The unclear length is between $10.4\ cm$ and $10.5\ cm$
We mentally divide the $1\ mm$ division in $10$ equal parts. We may note down the reading as $10.46\ cm$.
The digits $1,0,4$ are reliable and $6$ is doubtful.
So, the number of significant digits are,
Number of significant digits $=$ Number of reliable digit $+$ First uncertain digit
$$S = 3 + 1$$
$$S = 4$$
$$S = 4$$
Note:
- Significant figures indicate the precision of measurement which depends on the least count of the measuring instrument.
- The measurement that includes more digit than the significant digits is superfluous and also misleading about the precision of measurement.
