[dalke]

You do not understand correctly. Compare the ratio of the quadratic f(n) = 1E100 + n2 to the linear g(n) = 1E100 + n. Using n=100 and n=1000 the ratio is effectively 1.0. You need to get to n=100000000000000000000000000000000000000000000000000 before the ratio is 2.

[regularfry]

I see your point - we can compare the powers that n is raised to, but without knowing the constant factor we can't know the proportion of the result that it is responsible for.