Q- 16 What do you mean by significant figures and the rules of significant figures ?
Answer :-
Significant figures are meaningful digits which are known with certainty. The uncertainty is indicated bywriting the certain digits and the last uncertain digit. It is the maximum precision
(reliability of a measurement)
for a measurement. Thus, if we write a result as 11.2 mL, wesay the 11 is certain and 2 is uncertain and the uncertainty would be +1 in the last digit
There are certain rules for determining the number of significant figures. These are stated
below:
(1) All non-zero digits are significant. For example in 285 cm, there are three significant figures and in 0.25 mL, there are two significant figures.
(2) Zeros preceding to first non-zero digit are not significant. Such zero indicates the position of decimal point. Thus, 0.03 has one significant figure and 0.0052 has two significant figures.
(3) Zeros between two non-zero digits are significant. Thus, 2.005 has four significant figures.
(4) Zeros at the end or right of a number are significant provided they are on the right side of the decimal point. For example, 0.200 g has three significant figures. But, if otherwise, the zeros are not significant. For example, 100 has only one significant figure.
(5) Exact numbers have an infinite number of significant figures. For example, in 2 balls or 20 eggs, there are infinite significant figures as these are exact numbers and can be represented by writing infinite number of zeros after placing a decimal i.e., 2 = 2.000000 or 20 = 20.000000 When numbers are written in scientificnotation, the number of digits between 1 and10 gives the number of significant figures.Thus, 4.01×102 has three significant figures, and 8.256 × 10–3 has four significant figures.
Addition and Subtraction of SignificantFigures
The result cannot have more digits to the right of the decimal point than either of the original numbers.
12.11 + 18.0 + 1.012 = 31.122
Here, 18.0 has only one digit after the decimal point and the result should be reported only up to one digit after the decimal point which is 31.1.
Multiplication and Division of Significant Figures
In these operations, the result must be reported with no more significant figures as are there in the measurement with the few significant figures 2.5×1.25 = 3.125 Since 2.5 has two significant figures, theresult should not have more than two significant figures, thus, it is 3.1.
