Dimensionless numbers are numerical values that do not have any physical units associated with them. They are used in various fields of science and engineering to compare different systems or phenomena without the influence of specific units. Examples include the Reynolds number, which helps predict flow patterns in fluid dynamics, and the Mach number, which compares the speed of an object to the speed of sound. These numbers simplify complex relationships by providing a way to analyze and understand systems in a more universal manner. By using dimensionless numbers, researchers can identify similarities between different scenarios, making it easier to apply findings from one context to another.