Back to the theme of divisibility of numbers. Since we have the idea of writing numbers with a small set of digits, and with the place of those digits carrying information about how big the number is, we can think about what’s implied by that information.

In the number 222, the first two is matched to blocks (hundreds) that are ten times as large as those for the second two (tens), and the second two is matched to units (tens) which are ten times as large as those for the third two (units). It is now extremely rare to have the size of those blocks differ from one place to the next; that is, a number before the initial two here we take without needing it made explicit to represent ten times that hundreds unit, and a number after the final two (and therefore after the decimal point) would represent units which are one-tenth that of the final two’s size.

It has also become extremely rare for the relationship between blocks to be anything but a factor of ten, with two exceptions which I’ll mention next paragraph. The only block other than those with common use which comes to my mind is the sixty-to-one division of hours or degrees into minutes, and then of minutes into seconds. Even there the division of degrees of arc into minutes and seconds might be obsolete, as it’s so much easier on the computer to enter a latitude and longitude with decimals instead. So blocks of ten, decimals, it is, or in the way actual people speak of such things, a number written in base ten.

Continue reading “Bases For Comparison”

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