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单词 decimal representation
释义

decimal representation

(decimal expansion) Any real number a between 0 and 1 has a decimal representation, written 0.d1 d2 d3…, where each di is one of the digits 0, 1, 2,…, 9; this means that

This notation can be extended to enable any positive real number to be written as

using, for the integer part, the normal representation cncn−1…c1c0 to base 10 (see base). If, from some stage on, the representation consists of the repetition of a string of one or more digits, it is called a recurring or repeating decimal. For example, the recurring decimal 0.12748748748…can be written as inline or as inline, where the dots above indicate the beginning and end of the repeating string. If the repeating string consists of a single zero, this is generally omitted and the representation is called a terminating decimal.

The decimal representation of any real number is unique except for terminating decimals which have two expansions, as with 0.25 and inline. The numbers that can be expressed as recurring (including terminating) decimals are precisely the rational numbers.

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更新时间:2025/4/29 18:55:34