Why do we use base ten?
Because we have ten digits on our hands. Maybe a shrug or open palms to mean “nothing”.
But base ten has nine digits: 1 to 9 and a 0 for nothing.
Because we have ten digits on our hands. Maybe a shrug or open palms to mean “nothing”.
But base ten has nine digits: 1 to 9 and a 0 for nothing.
The theory is they did this because of their hands, but used one hand to count digits and the other hand to count groups of digits: for each of the 4 fingers they are divided into 3 segments. When you are counting, you can point to the four fingers with your thumb, thus giving 12 and a pointer to which finger you are on. Then in your other hand you can keep track of how many units of 12, so 5*12 = 60. A base 60 system. But there was no digit for zero, although of course they had a way of dealing with zero, it was just not considered a number.
Babylonians, for example, didn't conceptualize 0 as a numeric quantity just like 1 or 5. So, when they invented a sign for gaps in the numbers, they didn't use it at the ending positions, so their "I" could mean 1, or 60, or 3600, or..., depending on the context. Neither was it used to signify the quantity of zero: empty space was used instead.
What’s quite interesting is to ask pupils to assign numbers to their fingers and thumbs:
1 2 3 4 5 6 7 8 9 ... X?
It’s a good way of introducing positional number systems, and the... paradox? quandary? quirk?.. of how base N never includes a symbol for N, and how N in base N is always ‘10’.
See also: asking pupils to divide 12345* by 67, taught in the context of arithmetic and logical shifting.
(*base 67)