linguistic:translation
Positional notation

In modern positional numbers systems, such as the decimal system, the digits and their positions in the representation of an integer, for example, 45, are a shorthand notation for a polynomial in the radix or base, in this case, 4 × 10 + 5 × 10. As another example, in radix 5, a string of digits such as 132 denotes the (decimal) number 1 × 5 + 3 × 5 + 2 × 5 = 42. This representation is unique. Let b be a positive integer greater than 1. Then every positive integer a can be expressed uniquely in the form

a = r m b m + r m − 1 b m − 1 + ⋯ + r 1 b + r 0, {\displaystyle a=r_{m}b^{m}+r_{m-1}b^{m-1}+\dotsb +r_{1}b+r_{0},} where m is a nonnegative integer and the r' s are integers such that

0 < r < b and 0 ≤ r < b for i = 0, 1,..., m − 1.