This article explores the historical development of arithmetic and numeral systems from ancient civilizations to the period of scientific flourishing in the Islamic world. It highlights how fundamental concepts such as place value, zero, fractions, and computational tools emerged and evolved within diverse cultural contexts and practical needs. The study begins with the Babylonian sexagesimal system, one of the earliest known positional numeral systems, which enabled sophisticated calculations—particularly in astronomy—through its place-value structure. In contrast, the Greek alphanumeric system represents a non-positional approach to number representation, although sexagesimal divisions were adopted in astronomical computations.



The article then examines the origin of the decimal positional system in India, characterized by distinct numerals and the use of zero as a placeholder. This innovation marked a turning point in the history of mathematics. Through scientific and cultural exchanges, the decimal system was transmitted to the Islamic world, where it was not only adopted but further refined and systematized. Within this intellectual environment, structured algorithms for addition, subtraction, multiplication, and division were developed and widely applied in commerce, administration, and the sciences.



Special attention is given to the role of computational tools—particularly the dust board—in shaping arithmetic procedures. The material constraints and practical features of this device influenced the design of algorithms and calculation techniques. The gradual transition from dust boards to paper and ink represented not merely a technical shift but also a cultural transformation in the production and transmission of knowledge. Another significant development discussed is the formulation and consolidation of decimal fractions, which enhanced numerical precision and expanded the scope of quantitative reasoning.



Ultimately, the article argues that the evolution of numeral systems was not simply the invention of new symbols, but the result of a dynamic interaction between practical demands conceptual innovation, and material instruments of calculation. This long-term process laid the foundation for the shared mathematical language used worldwide today and underscores the interconnected contributions of multiple civilizations.