In multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures. Thus, in the example above, density should be reported to three significant figures. Density .237g . cm .
g cm - Similarly, if the speed of light is given as . × m s - (three significant figure) and one year (1y = . d) has . × s ( five significant figures), the light year is .
× m ( three significant figures). ( ) In addition or subtraction, the final result should retain as many decimal places as are there in the number with the least decimal places. For example, the sum of the numbers . g, .
g and . g by mere arithmetic addition, is . g. But the least precise measurement ( .
g) is correct to only one decimal place. The final result should, therefore, be rounded off to . g. Similarly, the difference in length can be expressed as : .
m – . m = . m = × – m. Note that we should not use the rule ( ) applicable for multiplication and division and write g as the result in the example of addition and .
× – m in the example of subtraction . They do not convey the precision of measurement properly. For addition and subtraction, the rule is in terms of decimal places. .
. Rounding off the Uncertain Digits The result of computation with approximate numbers, which contain more than one uncertain digit, should be rounded off. The rules for rounding off numbers to the appropriate significant figures are obvious in most cases. A number .
rounded off to three significant figures is . , while the number . would be . .
The rule by convention is that the preceding digit is raised by if the insignificant digit to be dropped (the underlined digit in this case) is more than , and is left unchanged if the latter is less than .