??? Presumably this number base makes sense to us because
we have 10 fingers. If our species had evolved with 12 fingers, we would probably have 2 more digits among
the set of symbols we use, and we would find it quite natural to compute sums in base 12. However, we have
only 10 fingers, so let??™s start with base 10.
Remember what the columns mean when we write a number like 427. The seven means we have 7 units,
the two means we have 2 tens, and the four means we have 4 hundreds. The total quantity is 4 hundreds, plus
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2 tens, plus 7. The column on the far right is for units (which you can also write as 100), the next column to the
left is for 10s (which you can also write as 101), and the next column is for 100s (which you can write as 102).
We say that we use ???base 10??? because the columns correspond to powers of 10??”100, 101, 102, etc.
Suppose that we had evolved with 12 fingers and were more comfortable working in base 12, instead. What
would the meaning of 427 be? The seven would still mean 7 units (120 is also equal to 1), but now the two would
mean 2 dozen (121 equals 12), and the four would mean 4 gross (122 equals 144). The value of the number 427
in base 12 would be 4 gross, plus 2 dozen, plus 7, or 607 in our more familiar base-10 representation.
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