Monte Carlo (MC) simulation is widely used in many different disciplines in order to analyze problems that involve uncertainty. Simulation decomposition has recently provided a simple, but powerful, advancement to the standard Monte Carlo approach. Its value for better informing decision making has been previously shown in the investment-analysis field. In this paper, we demonstrate that simulation decomposition can enhance problem analysis in a wide array of domains by applying it to three very different disciplines: geology, business, and environmental science. Further extensions to such disciplines as engineering, natural sciences, and social sciences are discussed. We propose that by incorporating simulation decomposition into pedagogical practices, we expect students to significantly advance their problem-understanding and problem-solving skills.