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# Decimal numeral system

(Redirected from Decimal expansion)

The decimal numeral system is a place-value notation for the representation of numbers using the powers of 10. It has become the numeral system of choice for humans, which could conveniently use their two hands times five fingers for counting.

The decimal representation of a real number ${\displaystyle \scriptstyle n\,}$ corresponds to the series

${\displaystyle n=\sum _{i=-\infty }^{k}d_{i}\,10^{i}=\left\{\sum _{i=-\infty }^{-1}d_{i}\,10^{i}\right\}+\left\{\sum _{i=0}^{k}d_{i}\,10^{i}\right\},\,}$

with decimal digits ${\displaystyle \scriptstyle d_{i}\,\in \,\{0,\,...,\,9\}\,}$, where the first term is the fractional part and the second term is the integer part.

Computers of course typically use the binary numeral system (although some have used the balanced ternary numeral system) for their internal computations, while input/output is conveniently done in decimal.

Most of Mathematica's built-in digit manipulation functions can use bases from 2 to 36, but when the user does not specify a base, those functions default to decimal. Users can mimic this behavior for their own user-defined functions by including something like b_:10 in their function definition.

Most of the keyword:base sequences in the OEIS pertain to decimal. For example, A004086, which takes the decimal digits of ${\displaystyle n}$ and reinterprets them read backwards.