Recurring Decimal
A repeating decimal or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero. It can be shown that a number is rational if and only if its decimal representation is repeating or terminating (i.e. all except finitely many digits are zero). For example, the decimal representation of becomes periodic just after the decimal point, repeating the single digit "3" forever, i.e. 0.333.... A more complicated example is , whose decimal becomes periodic at the ''second'' digit following the decimal point and then repeats the sequence "144" forever, i.e. 5.8144144144.... At present, there is no single universally accepted notation or phrasing for repeating decimals. The infinitely repeated digit sequence is called the repetend or reptend. If the repetend is a zero, this decimal representation is called a terminating decimal rather than a repeating decimal, since the zeros ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Decimal Representation
A decimal representation of a non-negative real number is its expression as a sequence of symbols consisting of decimal digits traditionally written with a single separator: r = b_k b_\ldots b_0.a_1a_2\ldots Here is the decimal separator, is a nonnegative integer, and b_0, \ldots, b_k, a_1, a_2,\ldots are ''digits'', which are symbols representing integers in the range 0, ..., 9. Commonly, b_k\neq 0 if k > 1. The sequence of the a_i—the digits after the dot—is generally infinite. If it is finite, the lacking digits are assumed to be 0. If all a_i are , the separator is also omitted, resulting in a finite sequence of digits, which represents a natural number. The decimal representation represents the infinite sum: r=\sum_^k b_i 10^i + \sum_^\infty \frac. Every nonnegative real number has at least one such representation; it has two such representations (with b_k\neq 0 if k>0) if and only if one has a trailing infinite sequence of , and the other has a trailing infinite ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]