Order of approximation: Difference between revisions

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=== Zeroth-order ===

''Zeroth-order approximation'' is the term [[scientist]]s use for a first rough answer. Many [[Approximation#Science|simplifying assumptions]] are made, and when a number is needed, an order-of-magnitude answer (or zero [[significant figure]]s) is often given. For example, you might say "the town has '''a few thousand''' residents", when it has 3,914 people in actuality. This is also sometimes referred to as an [[order of magnitude|order-of-magnitude]] approximation. The zero of "zeroth-order" represents the fact that even the only number given, "a few", is itself loosely defined.

A zeroth-order approximation of a [[function (mathematics)|function]] (that is, [[mathematics|mathematically]] determining a [[formula]] to fit multiple [[data point]]s) will be [[Constant (mathematics)|constant]], or a flat [[line (mathematics)|line]] with no [[slope]]: a polynomial of degree 0. For example,