chapter  19
10 Pages

A Different Way of Counting; Geometric Numbers

WithMalcolm E Lines

Readers who have progressed this far in the book are by now familiar with the shorthand ‘exponent’ notation used for many tens multiplied together. We have found it convenient to write one million (1,000,000) as 106 and one billion (1,000,000,000) as 109. Although this scheme is less of a shorthand when we get down to smaller numbers like 100 = 10 2 and 10 = 10 1 it is still nonetheless perfectly consistent and is really only another way of counting. We shall refer to it as counting geometrically (in contrast to the common system used in everyday experience which now, in order to distinguish it, we shall refer to as counting arithmetically). In geometric counting we are therefore already familiar with the meaning of the positive integers as follows:

Geometric Counting

Equivalent Arithmetic Number

1

10

2

100

3

1,000

4

10,000

5

100,000

6

1,000,000