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 – Some 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.
x = 123 has three significant figures.
Rule 2. All zeros occurring between two non zero digits are significant.
Example : x = 1002 has four significant figures.
x = 1.0203 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 = 0.0012 has only two significant digits.
x = 1.0012 has five significant figures. This is according rule 2.
Rule 4. All zeros on the right of the last non zero digit in the decimal part are significant.
Example : x = 0.00500 has three significant figures 5, 0, 0. The zeros before 5 are not significant.
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.
x = 234000 has three significant figures.
Rule 6. All zeros on the right of the last non zero digit become significant.
Example : Suppose distance between two place is measured to be 5030 m. It has four significant figures.
The same distance can be expressed as 5.030 km or 5.030×105 cm. 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 = 6.82 is rounded off to 6.8,
x = 8.94 is rounded off to 8.9.
Rule 2. If the digit to be dropped is more than 5, then the preceding digit is raised by one.
Example : x = 4.87 is rounded off to 4.9, x = 123.76 is rounded off to 123.8.
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 = 53.251 is rounded off to 53.3, x = 7.659 is rounded off to 7.7.
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 = 6.450 becomes 6.4 on rounding off, x = 24.650 becomes 24.6 on rounding off.
How many significant figures should be present in the answer of the following calculations?
(i) 
(ii) 5 × 5.364
(iii) 0.0125 + 0.7864 + 0.0215
Answer
(i)
Least precise number of calculation = 0.112
Number of significant figures in the answer
= Number of significant figures in the least precise number = 3
(ii) 5 × 5.364
Least precise number of calculation = 5.364
Number of significant figures in the answer = Number of significant figures in 5.364 = 4
(iii) 0.0125 + 0.7864 + 0.0215
Since the least number of decimal places in each term is four, the number of significant figures in the answer is also 4.
What do you mean by significant figures?
Significant figures are those meaningful digits that are known with certainty.
They indicate uncertainty in an experiment or calculated value. For example, if 15.6 mL is the result of an experiment, then 15 is certain while 6 is uncertain, and the total number of significant figures are 3.
Hence, significant figures are defined as the total number of digits in a number including the last digit that represents the uncertainty of the result.
Express the following in the scientific notation:
(i) 0.0048
(ii) 234,000
(iii) 8008
(iv) 500.0
(v) 6.0012
- (i) 0.0048 = 4.8× 10–3
- (ii) 234, 000 = 2.34 ×105
- (iii) 8008 = 8.008 ×103
- (iv) 500.0 = 5.000 × 102
(v) 6.0012 = 6.0012
How many significant figures are present in the following?
(i) 0.0025
(ii) 208
(iii) 5005
(iv) 126,000
(v) 500.0
(vi) 2.0034
- (i) 0.0025 There are 2 significant figures.
- (ii) 208 There are 3 significant figures.
- (iii) 5005 There are 4 significant figures.
- (iv) 126,000 There are 3 significant figures.
- (v) 500.0 There are 4 significant figures.
- (vi) 2.0034 There are 5 significant figures.
Round up the following upto three significant figures:
(i) 34.216
(ii) 10.4107
(iii) 0.04597
(iv) 2808
(i) 34.2
(ii) 10.4
(iii) 0.0460
(iv) 2810