Just adding to the other answers here (see no point in repeating information that's already well presented) - several other bases used in various cultures and civilizations, including 60, 20, 5, 4, binary, 12, and (unusually) base 27.
We have traces of base 60 in the number of degrees in a circle (360) and of minutes in an hour and seconds in a minute.
With some of those examples then the system might not have been used for very large numbers. I'm not sure if they all strictly count as "positional notation". Especially, I'd have thought, isn't really a positional system, properly speaking unless they count as far as 100 in the notation. And to be a positional system properly you need a concept of 0, or blank, or some way of writing numbers in a perfectly general way.
But some definitely count as positional - would say the ancient Babylonian base 60 is a reasonably fully fledged alternative base positional system for instance. Didn't use 0 as we do but had a placeholder apparently, or left gaps though not in a very consistent way
The gap between the 6 and the 9 to the right may be a hint of the "o"
Babylonian numerals (MacTutor)
(and wikipedia article Babylonian numerals)
See the wikipedia article on https://en.wikipedia.org/wiki/Po... and its section on Positional notation#Applications
also Duodecimal
And for the base 27 system based on counting body parts, so 27 = "one man" see Base 27.
(Wikipedia articles of course should be used with a bit of caution, if interested in some particular point follow up to the citation).
Counting on Your Body in Papua New Guniea
Though not exactly a "positional notation", in the old £ s d we had a mixed system of four farthings to a penny, twelve pennies to a shilling and twenty shillings to a pound, also had a florin consisting of two shillings.
Similarly for other systems of weights and measures, often mix of different numbers e.g. in the old UK version of the Avoirdupois system, which I learned as a school child in the UK in the 1970s,
16 drams make an ounce,
16 ounces make a pound,
14 pounds make a stone,
2 stones make a quarter,
four quarters make a hundredweight,
twenty hundredweight make a ton.
We all had that drilled into us when I was young, well apart from the 16 drams make an ounce, don't remember that bit.
We have traces of base 60 in the number of degrees in a circle (360) and of minutes in an hour and seconds in a minute.
With some of those examples then the system might not have been used for very large numbers. I'm not sure if they all strictly count as "positional notation". Especially, I'd have thought, isn't really a positional system, properly speaking unless they count as far as 100 in the notation. And to be a positional system properly you need a concept of 0, or blank, or some way of writing numbers in a perfectly general way.
But some definitely count as positional - would say the ancient Babylonian base 60 is a reasonably fully fledged alternative base positional system for instance. Didn't use 0 as we do but had a placeholder apparently, or left gaps though not in a very consistent way
The gap between the 6 and the 9 to the right may be a hint of the "o"
Babylonian numerals (MacTutor)
(and wikipedia article Babylonian numerals)
See the wikipedia article on https://en.wikipedia.org/wiki/Po... and its section on Positional notation#Applications
also Duodecimal
And for the base 27 system based on counting body parts, so 27 = "one man" see Base 27.
(Wikipedia articles of course should be used with a bit of caution, if interested in some particular point follow up to the citation).
Counting on Your Body in Papua New Guniea
MIXED NOTATION
Though not exactly a "positional notation", in the old £ s d we had a mixed system of four farthings to a penny, twelve pennies to a shilling and twenty shillings to a pound, also had a florin consisting of two shillings.
Similarly for other systems of weights and measures, often mix of different numbers e.g. in the old UK version of the Avoirdupois system, which I learned as a school child in the UK in the 1970s,
16 drams make an ounce,
16 ounces make a pound,
14 pounds make a stone,
2 stones make a quarter,
four quarters make a hundredweight,
twenty hundredweight make a ton.
We all had that drilled into us when I was young, well apart from the 16 drams make an ounce, don't remember that bit.
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