How big is a large number? How far can our imagination go to think or to imagine a large number? This work is part of the study of didactic approaches aimed at the knowledge of unimaginable numbers in secondary school. The topic is very interesting because this numbers very large, but finite numbers can be transitioned in the passage of the concrete transition from the concept of finite to that of infinity. This work is placed in continuity with the previous case studies carried out on the computational arithmetic of infinity. Specifically, a further case study is shown here: the planning phase contains identification regarding research questions and additional aspects including choice of case study method and discovering strengths or limitations. The case study design linked together from the beginning until the end, including everything from hypothesis and question design to data analysis and conclusion. In addition, it is showed the unit of analysis concerning the case study, the method by which these numbers together with their characteristics will be exhibiting order to give an idea of their estimated size, even with regard to the physical universe. Finally, the effects and results in terms of educational implications will be evaluated through the analysis of the results that emerged from the administration of a questionnaire proposed to the students of the classes involved.