“decimal representation”的概念、定义、翻译、参考文献-科学参考

decimal representation

Mathematics

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

$a = d_{1} \times 10^{- 1} + d_{2} \times 10^{- 2} + d_{3} \times 10^{- 3} + \dots .$

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

$c_{n} c_{n - 1} \dots c_{1} c_{0} . d_{1} d_{2} d_{3} \dots$

using, for the integer part, the normal representation c_nc_n−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 $0.12 \overset{——}{748}$ or as $0. 12 \dot{7} 4 \dot{8}$ , 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 $0.24 \dot{9}$ . The numbers that can be expressed as recurring (including terminating) decimals are precisely the rational numbers.

单词	decimal representation
释义	decimal representation Mathematics Any real number a between 0 and 1 has a decimal representation, written 0.d₁ d₂ d₃…, where each d_i is one of the digits 0, 1, 2,…, 9; this means that $a = d_{1} \times 10^{- 1} + d_{2} \times 10^{- 2} + d_{3} \times 10^{- 3} + \dots .$ This notation can be extended to enable any positive real number to be written as $c_{n} c_{n - 1} \dots c_{1} c_{0} . d_{1} d_{2} d_{3} \dots$ using, for the integer part, the normal representation c_nc_n−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 $0.12 \overset{——}{748}$ or as $0. 12 \dot{7} 4 \dot{8}$ , 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 $0.24 \dot{9}$ . The numbers that can be expressed as recurring (including terminating) decimals are precisely the rational numbers.
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