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A repeating decimal or recurring decimal is a decimal representation of a number whose digits are eventually periodic (that is, after some place, the same sequence of digits is repeated forever); if this sequence consists only of zeros (that is if there is only a finite number of nonzero digits), the decimal is said to be terminating, and is not considered as repeating.
1 ⁄ 3 = 0.33333... 1 ⁄ 7 = 0.142857142857... 1318 ⁄ 185 = 7.1243243243... Every time this happens the number is still a rational number (i.e. can alternatively be represented as a ratio of an integer and a positive integer). Also the converse is true: The decimal expansion of a rational number is either finite, or endlessly repeating.
The Natural Area Code, this is the smallest base such that all of 1 / 2 to 1 / 6 terminate, a number n is a regular number if and only if 1 / n terminates in base 30. 32: Duotrigesimal: Found in the Ngiti language. 33: Use of letters (except I, O, Q) with digits in vehicle registration plates of Hong Kong. 34
Some programming languages (or compilers for them) provide a built-in (primitive) or library decimal data type to represent non-repeating decimal fractions like 0.3 and −1.17 without rounding, and to do arithmetic on them. Examples are the decimal.Decimal or num7.Num type of Python, and analogous types provided by other languages.
Thus 123.456 is considered an approximation of any real number greater or equal to 1234555 / 10000 and strictly less than 1234565 / 10000 (rounding to 3 decimals), or of any real number greater or equal to 123456 / 1000 and strictly less than 123457 / 1000 (truncation after the 3. decimal). Digits that suggest a ...
Like the binary floating-point formats, the number is divided into a sign, an exponent, and a significand. Unlike binary floating-point, numbers are not necessarily normalized; values with few significant digits have multiple possible representations: 1×10 2 =0.1×10 3 =0.01×10 4, etc. When the significand is zero, the exponent can be any ...
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