trailing zero(s) in the base number a . They are always significant. ( ) The scientific notation is ideal for reporting measurement. But if this is not adopted, we use the rules adopted in the preceding example : For a number greater than , without any decimal, the trailing zero(s) are not significant.
For a number with a decimal, the trailing zero(s) are significant. ( ) The digit conventionally put on the left of a decimal for a number less than (like . ) is never significant. However, the zeroes at the end of such number are significant in a measurement.
( ) The multiplying or dividing factors which are neither rounded numbers nor numbers representing measured values are exact and have infinite number of significant digits. For example in d r = or s = π r , the factor is an exact number and it can be written as . , . or .
as required. Similarly, in t T n , n is an exact number. . .
Rules for Arithmetic Operations with Significant Figures The result of a calculation involving approximate measured values of quantities (i.e. values with limited number of significant figures) must reflect the uncertainties in the original measured values. It cannot be more accurate than the original measured values themselves on which the result is based. In general, the final result should not have more significant figures than the original data from which it was obtained.
Thus, if mass of an object is measured to be, say, . g (four significant figures) and its volume is measured to be . cm , then its density, by mere arithmetic division, is .68804780876 g/cm upto decimal places. It would be clearly absurd and irrelevant to record the calculated value of density to such a precision when the measurements on which the value is based, have much less precision.
The following rules for arithmetic operations with significant figures ensure that the final result of a calculation is shown with the precision that is consistent with the precision of the input measured values : ( )