information:classification, structural:reformatting, linguistic:voice_change
Notation

There are several different conventions for writing p -adic expansions. So far this article has used a notation for p -adic expansions in which powers of p increase from right to left. With this right-to-left notation the 3-adic expansion of 1 5, {\displaystyle {\tfrac {1}{5}},} for example, is written as

When performing arithmetic in this notation, digits are carried to the left. It is also possible to write p -adic expansions so that the powers of p increase from left to right, and digits are carried to the right. With this left-to-right notation the 3-adic expansion of 1 5 {\displaystyle {\tfrac {1}{5}}} is

p -adic expansions may be written with other sets of digits instead of {0, 1,..., p − 1 }. For example, the 3 -adic expansion of 1 5 {\displaystyle {\tfrac {1}{5}}} can be written using balanced ternary digits { 1, 0, 1 }, with 1 representing negative one, as

In fact any set of p integers which are in distinct residue classes modulo p may be used as p -adic digits. In number theory, Teichmüller representatives are sometimes used as digits.

Quote notation is a variant of the p -adic representation of rational numbers that was proposed in 1979 by Eric Hehner and Nigel Horspool for implementing on computers the (exact) arithmetic with these numbers.