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:''This article gives a mathematical definition. For a more accessible article see Decimal.'' A decimal representation of a non-negative real number ''r'' is an expression in the form of a series, traditionally written as a sum : where ''a''0 is a nonnegative integer, and ''a''1, ''a''2, ... are integers satisfying 0 ≤ ''ai'' ≤ 9, called the digits of the decimal representation. The sequence of digits specified may be finite, in which case any further digits ''a''''i'' are assumed to be 0. Some authors forbid decimal representations with a trailing infinite sequence of "9"s. This restriction still allows a decimal representation for each non-negative real number, but additionally makes such a representation unique. The number defined by a decimal representation is often written more briefly as : That is to say, ''a''0 is the integer part of ''r'', not necessarily between 0 and 9, and ''a''1, ''a''2, ''a''3, ... are the digits forming the fractional part of ''r''. Both notations above are, by definition, the following limit of a sequence: :. ==Finite decimal approximations== Any real number can be approximated to any desired degree of accuracy by rational numbers with finite decimal representations. Assume . Then for every integer there is a finite decimal such that : Proof: Let , where . Then , and the result follows from dividing all sides by . (The fact that has a finite decimal representation is easily established.) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「decimal representation」の詳細全文を読む スポンサード リンク
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