Q: Why is the bond order in some molecules in fraction and not a whole number. For example a molecule having bond order 1.5 . What is its physical significance . And moreover will we consider it to be a single bond or a double bond.

When you are talking about the molecular orbital theory(MOT) than bond order explain the stability of  molecules but when you talk about the atomic orbital theory than bond order can describe the number of bonds exist between the atoms.So,in M.O.T(exist in molecules only) bond order which is positive means only that the molecule is stable.Fraction or whole number doesn't have any significance, only positive/negative value need to be consider.