Quantitative K-theory is a refinement of ordinary operator K-theory.  It was developed by Guoliang Yu in his work on the Novikov conjecture for groups with finite asymptotic dimension, and has been studied systematically by Oyono-Oyono and Yu. To explore a way of approximating K-theory with quantitative K-theory, Oyono-Oyono and Yu studied the persistence approximation property for quantitative K-theory of filtered C∗-algebras. In this talk, we extend these methods and results to Lp operator algebras. This is a joint work with Hang Wang, Yanru Wang and Jianguo Zhang.