Write and explain rules of determining significant digit with example.

Explanation

Determining significant digit rules are as follows:
(a) All the non-zero digit are significant. In 584 there are 3 significant digit.
(b) All the zeros between two non-zero digits are significant no matter where the decimal point is, if at all
In 120007 cm, 1, 2, 0, 0, 0 and 7 total 6 digit are significant digit.
(c) The trailing (or terminal) zero(s) in a number without a decimal point are not significant.
123 m = 12300 cm = 123000 mm no. of significant digit are three (3).
(d) If the number is less than 1, the zero (s) on the right of the decimal point but to the left of the first non-zero digit are not significant. In 0.0 02308 underlined zeros are not significant
(e) In number with decimal point trailing zero are significant. Example: In 3.500 cm, 3, 5, 0, 0 total digit are significant.
In 0.0 6990 underlined zero are not significant but trailing zero is significant
`:.` Total 4 digit 6, 9, 9, 0 are significant.
(2) When measurement are represented with trailing zero, its aim is to represent measurement with more accuracy. Hence, it should be considered as significant digit. For example, 4.700 m 470.0 cm = 4700 mm here in each case number significant digit are 4 (four).
To remove ambiguities determining the number of significant figures, the best way is to report every measurement in scientific notation. (In the power of 10).
In this notation every number is represented as `axx 10^(b)` where a is number between 1 and 10 and bis any positive or negative exponent (power) of 10.
For example, 246.35 kg is represented in scientific notation as `2.4635 xx 10^(2)`
In scientific notation is best method for representing any measurement. But here also we have to follow rules of significant figure.
(i) For a number greater than 1 without any decimal the trailing zero are not significant.
(ii) For a number with decimal the trailing zero are significant.
The digit 0 put on a left of a decimal is not significant but trailing zero are significant.
In multiplication in number representing measured value are exact and have infinite number of significant digits.
For example, `s= 2pi r r=(d)/(2)` factor 2 is an exact no hence it can be written as 2 or 2.0 or 2.000 as required.
Similarly in `T=(t)/(n)` n is exact number (no. of revolution)
(6) In process of division if denominator is a fixed number then it can have infinite no. of significant digit.