I am reading the paper "Enzyme kinetics for a two-step enzymic reaction with comparable initial enzyme-substrate ratios" by C. L. Frenzen and P. K. Maini, where they nondimensionalize a system of differential equations.
They keep writing "unit order of magnitude" - what does this exactly mean?
For example, they write
"We nondimensionalize the dependent and independent variables by letting $$S = \alpha s, Y = \pi y,$$ where $s$ and $y$ are dimensionsless variables, and $\alpha$ and $\pi$ are appropriate scales for the dependent variables. We will endeavour to choose $\alpha$ and $\pi$ so that s and y are of unit order of magnitude ..."
