Order of approximation

Zeroth order approximation (also 0^th order) is the term scientists use for a first educated guess at an answer. Many simplifying assumptions are made, and when a number is needed, an order of magnitude answer (or no significant figures is often given. A zeroth order approximation of a function (that is, mathematically determining a formula to fit multiple data points) will be constant, or a flat line with no slope. For example,

$x=[0,1,4]$

$y=[0,1,2]$

$y\sim f(x)=1.67$

is an approximate fit to the data.

See also:

• First order approximation
• Second order approximation

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