Why can you neglect higher order terms as a variable tends to zero?

Question

If we have an expression involving various powers of some variable $x$, we often neglect 2nd or higher order terms as $x\to0$ as the higher powers become negligible compared to the lower powers. However the validity of this relies on the fact that $x<1$ so that $x^2<x$. This means that the values of $x$ for which the approximation is valid depends on the choice of units of $x$, which seems to make no sense at all! Does anyone have an explanation for this? Thanks :)

Answer 1

When $x\to 0$, independently by the dimensions since we are dealing with unitless quantity, we can assume WLOG that eventually $x<1$ then we have that $x^2<<x$.