Place value lets the same digit mean ones or hundreds
Positional notation makes a symbol's value depend on place as well as shape—each slot a power of the base. Roman numerals mostly add fixed symbols instead. Babylonians pioneered base-60 place value, still echoing in 60 minutes and 360-degree circles; binary place value runs nearly every computer.
Babylonian base-60 numbers are credited as the first positional system, but they lacked a real zero: at first the gap was inferred from context, and by about 700 BC a space or a pair of slanted wedges marked it, never alone or at the end of a number, so 2 and 120 looked identical. Archimedes built a decimal positional scheme on 10^8 in his Sand Reckoner, and Carl Gauss later lamented that he stopped short of the modern decimal system. Hellenistic and Roman astronomers kept to the Babylonian base 60.
The oldest surviving positional systems are Chinese rod numerals, in use by the early eighth century, or possibly Khmer numerals of the seventh. Both Khmer and other Indian numerals descend from Brahmi symbols of about the third century BC, which were not yet positional; medieval Indian numerals were, as are the Arabic numerals derived from them and attested from the tenth century. Decimal fractions appeared in Chinese rod calculus in the first century BC, and al-Uqlidisi used positional decimal fractions in Damascus in the mid-tenth century.
In Europe Simon Stevin's De Thiende usually gets credit for decimal fractions, though Regiomontanus anticipated them. Revolutionary France pushed decimalisation further; decimal time and a decimal calendar failed, but decimal currency and metric measures spread almost worldwide. In any base b the digits run from 0 to b − 1, so hexadecimal adds A through F, and 14B9 in base sixteen equals 5305 in base ten.
Source: Positional notation
