The strategy orlf approximation turned out to be very successful. (i) Most observed phenomena in daily life are rather complicated manifestations of the basic laws.(ii)Scientists recognised the importance of extracting the essential features of a phenomenon from its less significant aspects.(iii)It is not practical to take into account all the complexities of a phenomena in one go.(iv)A good strategy is to focus first on the essential features of a phenomena and discover the basic principles and then introduce corrections to build a more refined theory.(v)During study for free fall under gravity we assume air resistance to be zero.Similarly in mechanics we take moving objects as point objects.
The strategy of approximation can be explained as -[1]Speculation (talking about future results of experiments) and conjecture ( a approximation)have an important role to play during the procedure of scientific method of describing a phenomena, but must be verified by experiments.For example (i) The circular orbits as assumed by Nicolaus Copernicus in the heliocentric theory was replaced after certain inspections and experiments carried by Johannes Kepler.(ii)Paul Dirac in 1930, theoretically introduced the concept of antiparticle,which was later experimentally verified by Carl Anderson. [ii] Sometimes physical constants had to be assumed , their values later experimentally verified. The Universal gravitational constant G and constant in the coulombian force 1/4πε_0 were earlier assumed and later evaluated by using torsion balance.
Approximation theory is a branch of mathematics, a quantitative part of functional analysis. Approximation usually occurs when an exact form or an exact numerical number is unknown.