In the measured value of a physical quantity, the digits about the
correctness of which we are surplus the last digit which is doubtful, are
called the significant figures. Number of significant figures in a physical
quantity depends upon the least count of the instrument used for its
measurement.
(1) Common rules for counting significant figures Following are
some of the common rules for counting significant figures in a given
expression
Rule 1. All non zero digits are significant.
Example : x 1234
has four significant figures. Again
x 189
has only three significant figures.
Rule 2. All zeros occurring between two non zero digits are
significant.
Example :
x 1007
has four significant figures. Again
x 1.0809
has five significant figures.
Rule 3. In a number less than one, all zeros to the right of decimal
point and to the left of a non zero digit are not significant.
Example :
x 0.0084
has only two significant digits. Again,
x 1.0084
has five significant figures. This is on account of rule 2.
Rule 4. All zeros on the right of the last non zero digit in the
decimal part are significant.
Example :
x 0.00800
has three significant figures 8, 0, 0. The
zeros before 8 are not significant again 1.00 has three significant figures.
Rule 5. All zeros on the right of the non zero digit are not
significant.
Example :
x 1000
has only one significant figure. Again
x 378000
has three significant figures.
Rule 6. All zeros on the right of the last non zero digit become
significant, when they come from a measurement.
Example : Suppose distance between two stations is measured to be
3050 m. It has four significant figures. The same distance can be expressed
as 3.050 km or cm
5
3.050 10
. In all these expressions, number of
significant figures continues to be four. Thus we conclude that change in
the units of measurement of a quantity does not change the number of
significant figures. By changing the position of the decimal point, the
number of significant digits in the results does not change. Larger the
number of significant figures obtained in a measurement, greater is the
accuracy of the measurement. The reverse is also true.
(2) Rounding off : While rounding off measurements, we use the
following rules by convention
Rule 1. If the digit to be dropped is less than 5, then the preceding
digit is left unchanged.
Example :
x 7.82
is rounded off to 7.8, again
x 3.94
is
rounded off to 3.9.
Rule 2. If the digit to be dropped is more than 5, then the preceding
digit is raised by one.
Example : x = 6.87 is rounded off to 6.9, again x = 12.78 is rounded
off to 12.8.
Rule 3. If the digit to be dropped is 5 followed by digits other than
zero, then the preceding digit is raised by one.
Example : x = 16.351 is rounded off to 16.4, again
x 6.758
is
rounded off to 6.8.
Rule 4. If digit to be dropped is 5 or 5 followed by zeros, then preceding
digit is left unchanged, if it is even.
Example : x = 3.250 becomes 3.2 on rounding off, again
x 12.650
becomes 12.6 on rounding off.
Rule 5. If digit to be dropped is 5 or 5 followed by zeros, then the
preceding digit is raised by one, if it is odd.
Example : x = 3.750 is rounded off to 3.8, again
x 16.150
is
rounded off to 16.2.
(3) Significant figure in calculation
(i) Addition and subtraction : In addition and subtraction the
following points should be remembered
(a) Every quantity should be changed into same unit.
(b) If a quantity is expressed in the power of 10, then all the
quantities should be changed into power of 10.
(c) The result obtained after addition or subtraction, the number of
figure should be equal to that of least, after decimal point.
(ii) Multiplication and division
(a) The number of significant figures will be same if any number is
multiplied by a constant.
(b) The product or division of two significant figures, will contain
the significant figures equal to that of least.