Check out the p-adic numbers - http://en.wikipedia.org/wiki/P-adic_number http://en.wikipedia.org/wiki/P-adic_number : "Informally, most people are comfortable

Check out the p-adic numbers - http://en.wikipedia.org/wiki/P-adic_number http://en.wikipedia.org/wiki/P-adic_number : "Informally, most people are comfortable with non-terminating decimals because it is clear that a real number can be approximated to any required degree of closeness by a terminating decimal adequately expressed for its intended application. If two decimal expansions differ only after the 10th decimal place they are quite close to one another, and if they differ only after the 20th decimal place they are even closer." "10-adic numbers use a similar non-terminating expansion, but with a different concept of "closeness" (which mathematicians call a metric). Whereas two decimal expansions are close to one another if they differ by a large negative power of 10, two 10-adic expansions are close if they differ by a large positive power of 10. Thus 3333 and 4333 are close in the 10-adic metric, and 33333333 and 43333333 are even closer."