Editing Order of approximation (section)

===First-order===
''First-order approximation'' is the term scientists use for a slightly better answer.<ref name=":0" /> Some simplifying assumptions are made, and when a number is needed, an answer with only one significant figure is often given ("the town has {{val|4|e=3}}, or ''four thousand'', residents"). In the case of a first-order approximation, at least one number given is exact. In the zeroth-order example above, the quantity "a few" was given, but in the first-order example, the number "4" is given.

A first-order approximation of a function (that is, mathematically determining a formula to fit multiple data points) will be a linear approximation, straight line with a slope: a polynomial of degree&nbsp;1. For example:

: <math>x = [0.00, 1.00, 2.00],</math>
: <math>y = [3.00, 3.00, 5.00],</math>
: <math>y \sim f(x) = x + 2.67</math>

is an approximate fit to the data.
In this example there is a zeroth-order approximation that is the same as the first-order, but the method of getting there is different; i.e. a wild stab in the dark at a relationship happened to be as good as an "educated guess".