<P> Several authors in the last 300 years have noted a facility of positional notation that amounts to a modified decimal representation . Some advantages are cited for use of numerical digits that represent negative values . In 1840 Augustin - Louis Cauchy advocated use of signed - digit representation of numbers, and in 1928 Florian Cajori presented his collection of references for negative numerals . The concept of signed - digit representation has also been taken up in computer design . </P> <P> Despite the essential role of digits in describing numbers, they are relatively unimportant to modern mathematics . Nevertheless, there are a few important mathematical concepts that make use of the representation of a number as a sequence of digits . </P> <P> The digital root is the single - digit number obtained by summing the digits of a given number, then summing the digits of the result, and so on until a single - digit number is obtained . </P> <P> Casting out nines is a procedure for checking arithmetic done by hand . To describe it, let f (x) (\ displaystyle f (x)) represent the digital root of x (\ displaystyle x), as described above . Casting out nines makes use of the fact that if A + B = C (\ displaystyle A + B = C), then f (f (A) + f (B)) = f (C) (\ displaystyle f (f (A) + f (B)) = f (C)). In the process of casting out nines, both sides of the latter equation are computed, and if they are not equal the original addition must have been faulty . </P>

How important is the position of a digit in a number