Short answers, pulled from the story.
Babylonian scribes created the first positional numeral system over four thousand years ago. This system, known as sexagesimal, operated on a base of sixty and was carved into clay tablets. It fundamentally changed how humanity tracked time and space.
Scribes began using a space or a pair of slanted wedges to indicate a missing value around seven hundred BC. This symbol remained a placeholder rather than a number in its own right and could not stand alone at the end of a number. The true leap to a complete positional system required the invention of zero as a digit, which emerged for another millennium in the Indian subcontinent.
The Hindu-Arabic numeral system fully matured by the tenth century. This system utilized ten digits from zero through nine to represent any number with arbitrary precision. The introduction of zero allowed for the representation of negative numbers and fractions, enabling calculations that were previously too difficult for human minds to manage.
Simon Stevin published his textbook De Thiende in 1585. This work standardized the use of decimal fractions, allowing for the representation of numbers less than one with a simple separator. This innovation made arithmetic operations significantly simpler and faster, leading to the global dominance of the base-ten system we use today.
The Persian mathematician Jamshīd al-Kāshī advanced the use of decimal fractions in the fifteenth century. He created a system that allowed for the representation of numbers less than one with a simple separator. This innovation was crucial for the development of modern mathematics, as it enabled the precise calculation of fractions and the representation of irrational numbers.