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I have the following typed up so as to truncate higher powers of $\tau$,

1. x^2 τ^1. - 2. x y τ^1.5 + y^2 τ^2. + 
 2. x^2 τ^2. - 3. x y τ^2.5 + O τ^3 + 
 1. y^2 τ^3 + 2. x^2 τ^3. - 2. x y τ^3.5 + 
 0.25 y^2 τ^4 + 1. x^2 τ^4. - 0.5 x y τ^4.5 + 
 0.25 x^2 τ^5. + O[τ]^3

Unfortunately, the big-oh notation does not give me results that I expect. What am I doing wrong?

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The problem is floating-point powers. Rationalize solves the problem

Rationalize[
 1. x^2 τ^1. - 2. x y τ^1.5 + y^2 τ^2. + 
  2. x^2 τ^2. - 3. x y τ^2.5 + O τ^3 + 
  1. y^2 τ^3 + 2. x^2 τ^3. - 2. x y τ^3.5 + 
  0.25 y^2 τ^4 + 1. x^2 τ^4. - 0.5 x y τ^4.5 + 
  0.25 x^2 τ^5. + O[τ]^3]

enter image description here

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