Suppose the time period of a simple pendulum is 1.58 sec. The digits 1 and 5 are reliable and certain while the last digit 8 is uncertain. So the time period has three significant figures. Again suppose the mass of an object is measured as 125.7 gram. It has four significant figures the digits 1, 2 and 5 are reliable while the last digit 7 is uncertain.
If the length of an iron cylinder measured by a metre scale is 2.2 cm, it may be 2.17 cm when measured by vernier callipers and further 2.176 cm when measured by a micrometer screw gauge. The results written have 2, 3 and 4 figures respectively. It clearly shows that measuring instruments have least count 0.1 cm, 0.01 cm and 0.001 cm respectively. The figures (2, 3 and 4) in above examples are called significant figures. In these figures, the right most figure (digit) is reasonably correct while others are absolutely correct. The significant figures in a measured quantity indicate the number of digits in which we have confidence. From above discussion it is clear that the measurement of length 2.176 is more precise than 2.17 cm and 2.17 cm is more precise than 2.2 cm.
Following are the rules for determining the numbers of significant figures: All non-zero digits are significant. So 21.73 have four significant figures.
a. All non zero digits are significant . Thus, 300.04 gram has five significant figures.
b. All zeros between two non-zero digits are significant. Thus 300.04 gram has five significant figures.
c. All zeros to the right of non-zero digits but to the left of an understood decimal point are not significant. For example, 86400 have three significant figures. But such zeros are significant if they come from a measurement. For example, 86400 second has 5 significant figures.
d. All zeros to the right of the decimal point are significant. For example, 151 cm, 151.0 cm and
151.00 cm have three, four and five significant figures respectively.
e. All zeros to the right of the decimal point but to the left of a non-zero digit are not significant figures. For example, 0.181 cm and 0.0181 cm both have three significant figures.
f. The number of significant figures does not depend on the system of the units. For example 13.1 cm, 0.131 m and 0.000131 km all have three significant figures.
Significant Figures in Addition and Subtraction
When we add or subtract the numbers obtained from actual measurement, the result should have lowest decimal places or lowest significant figures, as that of input data. For example
Sum
327.6 + 15.22= 342.82
Difference
327.6 - 15.22 = 312.38
Since in both cases, the number to be added or subtracted consist four significant figures, the result should have four significant figures. Since here we have five significant figures in the result, the fifth number should be ignored. Rounding off should be done for the digit to be removed. Thus after rounding off, the correct result is: sum = 342.8 and difference = 312.4.
Significant Figures in Multiplication and Division
When we multiply or divide the numbers obtained from actual measurement, the result should have lowest significant figures, as that of input data .
For example,
214.6 * 15.2 = 3261.92