o
o
All zeros between two non-zero digits are significant irrespective of decimal place .
For a value less than 1 , zeroes after decimal and before non-zero digits are not significant . Zero before decimal place in such a number is always insignificant .
o Trailing zeroes in a number without decimal place are insignificant . o Trailing zeroes in a number with decimal place are significant . Cautions to remove ambiguities in determining number of significant figures
o Change of units should not change number of significant digits . Example , 4.700m = 470.0 cm = 4700 mm . In this , first two quantities have 4 but third quantity has 2 significant figures . o
o
Use scientific notation to report measurements . Numbers should be expressed in powers of 10 like a x 10 b where b is called order of magnitude . Example , 4.700 m = 4.700 x 10 2 cm = 4.700 x 10 3 mm = 4.700 x 10 -3 In all the above , since power of 10 are irrelevant , number of significant figures are 4 .
Multiplying or dividing exact numbers can have infinite number of significant digits . Example , radius = diameter / 2 . Here 2 can be written as 2 , 2.0 , 2.00 , 2.000 and so on .
Rules for Arithmetic operation with Significant Figures
Type
Multiplication or Division
Addition or Subtraction
Rule
The final result should retain as many significant figures as there in the original number with the lowest number of significant digits .
The final result should retain as many decimal places as there in the original number with the least decimal places .