Humans have the special gift of counting: I have five gold rings, and you have a dozen red roses and together we'll run hand in hand jumping two hundred and fifty six times through the park. These quantities can be written down in some fashion using a series of single numbers or digits: 5 gold rings, 12 red roses and 256 leaps. But what precisely do the digits "1", "2", "5" and "6" mean here?

What's in a number?

The quantities zero through nine can be written as numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. What then? We go back to zero and start with one in the next column: 10. Then we start over counting back up through to nine in our furthest right column and then once again the next column goes up (is incremented) by one and the rightmost column is back to zero: 20, on to 99 then 100, and so on and on.

This iterative process of going up to nine, then back to zero while incrementing the next-left column goes on indefinitely and we can express any positive (i.e. above zero) number we can imagine. Each column represents a number ten times as big as the last column: ten is ten times bigger than one, a hundred is ten times bigger than ten, a thousand is ten times bigger than a hundred, and so on.

Another way of looking at these columns is that each digit is that amount multiplied by how much the column represents, be it one, ten, hundred, or how ever much: 256 is (2 x 10 x 10) + (5 x 10) + 6.


Each of those columns which meant ten times ten times ... can be expressed with an exponent or power, or how many times the number in question is multiplied by itself: one hundred is ten times ten, or ten raised to the power of two, or just ten to the power of two, or even just ten to the two. And as a logical extension incidently, 1 is 100. In fact anything0 is one.

Base Ten

Humans currently* use a numbering system that's based on the number ten as we've seen. Why ten? Why not nine, or eleven? The conventional wisdom seems to be that it's because we have ten fingers & and thumbs, surely not by coincidence collectively referred to as "digits". I'm not aware of other theories although would be interested to hear any!

Let's explore bases some more, seeing what happens when we use a number other than ten...


When I said "currently" I'm imagining that we as a species, upon wide dissemination and global discussion of the information contained in these pages, will move to a numbering system based on twelve in the not too distant future :-)