First order approximation

First order approximation (also 1^st order) is the term scientists use for a further educated guess at an answer. Some simplifying assumptions are made, and when a number is needed, an answer with only one significant figure is often given. A first order approximation of a function (that is, mathematically determining a formula to fit multiple data points) will be a straight line with a slope. For example,

${\displaystyle x=[0,1,4]}$

${\displaystyle y=[0,1,2]}$

${\displaystyle y\sim f(x)=1.5*x}$

is an approximate fit to the data.

See also:

• Zeroth order approximation
• Second order approximation

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