How did the hindu-arabic number system work?

Answer 1

The same way it works today. The Hindu-Arabic numeral system is the system we use to notate numbers in everyday life, albeit with Latin glyphs rather than the original Indian symbols which descended from the Indian Brahmi numerals. Many regions still use their own traditional symbols, however the Latin glyphs are internationally recognised as the standard form of numeration today.

The Hindu-Arabic numeral system is positional, base-10, although it was originally base-9 given that there was no symbol for the number zero (a space was used as a place-holder). Although the concept of nothing was well established, mathematicians of the day did not regard zero to be a real number, thus it had no symbol, unlike all other numerals. In Latin, the word "nulla" was used in its place.

Prior to Hindu-Arabic, although there were many systems that were intrinsically decimal (including Roman numerals), they used special symbols for multiples of 10 (10, 20, 30, etc) as well as symbols for 100, 1,000 and so on. Reducing the symbol set to just 10 numeric symbols provided a concise notation that revolutionised computation and mathematics, particularly for those who were solely familiar with Roman numerals which do not easily lend themselves to computation, due to their intrinsically non-positional nature.

Despite the revolution, other numeric systems are still in place to this day. Many of us are familiar with binary numeric systems, as used in computers, along with the related hexadecimal and octal shorthand notation, however base-12 and base-60 are also in common use without us even realising it. Degrees, minutes and seconds, for instance, are all intrinsically base-60, due to its high divisibility with all the values 1, 2, 3, 4, 5 and 6, as well as 12, 15, 20 and 30. The only real difference today is that we no longer use complex sexagesimal symbols, we use simple variations of the Hindu-Arabic numeral system to notate all numbers, regardless of their base.