Significant figures
In measured value of the physical quantity, the digits regarding the correctness of which we are surplus the last digit which is doubtful, are called as the significant figures. Various of significant figures in a physical quantity depends upon least count of the instrument used for its measurement.
(1) The common rules for counting significant figures following are some of the common rules for counting the significant figures in a given expression
Rule 1. All the non zero digits are significant.
Example : x = 1234 contains four significant figures. Again x = 189 contains only three significant figures.
Rule 2. All the zeros occurring between the two non zero digits are significant.
Example : x = 1007 contains four significant figures. Again x = 1.0809 contains five significant figures.
Rule 3. In a number lesser than one, all the zeros to the right of decimal point and to the left of a non zero digit are not significant.
Example : x = 0.0084 contains only two significant digits. Again, x = 1.0084 contains five significant figures. This is on the account of rule 2.
Rule 4. All the zeros on the right of the last non zero digit in the decimal part are significant in nature.
Example : x = 0.00800 contains three significant figures which are 8, 0, 0. The zeros before 8 are not significant again 1.00 contains three significant figures.
Rule 5. All the zeros on the right side of the non zero digit are not significant.
Example : x = 1000 contains only one significant figure. Again x = 378000 contains three significant figures.
Rule 6. All the zeros on the right of the last non zero digit become important, when they come from a measurement.
Example : Assume distance between the two stations is measured to be 3050 m. It has four significant figures. The same distance can be expressed as 3.050 km or 3.050*105 cm. In all these expressions, number of important figures continues to be four. Hence we can conclude that change in the units of the measurement of a quantity does not change number of significant figures. By changing position of decimal point, the number of significant digits in the results remains unchanged. Larger the number of significant figures obtained in the measurement, greater is the accuracy of the measurement. The reverse of it is also true.
(2) Rounding off : While rounding off the measurements, we use the below written rules
Rule 1. If the digit to be dropped is lesser than 5, then the preceding digit is left without any change.
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 greater than the number 5, then the preceding digit is increased 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 the digits any term other than zero, then preceding digit is increased 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, after that the preceding digit is left without any change, 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 the digit to be dropped is 5 or 5 followed by the zeros, then the preceding digit is increased by one, if it is odd in nature.
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 are written below
(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 power of 10, then all quantities should be changed into power of 10.
(c) The result obtained after the addition or subtraction, the number of the figure should be equal to that of least, after a decimal point.
(ii) Multiplication and division
(a) The number of the significant figures will be same if any number is multiplied by a constant.
(b) The product or the division of two significant figures, will contain the significant figures equal to that of least.
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