Well as pundir rightly pointed it is the greatest integer less than

x = [x] + {x}

where,   [x] = Greatest Integer less than

               {x} = Fractional part

   where,  0 < {x} < 1 ( always)

[2.9] = [2] + {0.9}

[-1.3] = [ -2] + {0.7}       

PS:

we did not took -1, as then {x} would have been -0.3 which would not have been right  as  0 < {x} < 1                       

There is really simple way to remember this

Just truncate the decimal part when x is positive and

when negative ignore - sign and add one to digit and place - sign again

[2.01] becomes 2

and [-1.3] becomes -2

This is the easiest and most reliable short cut

what i told was an analytical way of expressing any number

This method of expression would help in some typical kind of question where you would need to express x as that form..

What you are suggesting is a way to find out [x] which i never contradicted....the easy method a consequence in itself , not a concept...