Decimal fraction: Difference between revisions
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{{for|the infinite decimal representation of a real number|Decimal}} |
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#REDIRECT [[Decimal]] |
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A '''decimal number''' is a number that becomes an integer, when multiplied by a sufficiently high [[exponentiation|power]] of 10. A '''decimal numeral''' is the standard representation of a decimal number in the [[Hindu-Arabic numeral]]. A decimal numeral consists of a (finite) sequence of [[decimal digit]]s representing an integer (the [[integer part]]), followed by a [[decimal mark]] (either dot "{{math|.}}" or comma "{{math|,}}", depending on the country), and another finite sequence of digits, the [[fractional part]]. For representing [[integer]]s, either the decimal mark and the fractional part are lacking, or the fractional part consists of one or several 0. For example, 32, 32.00, 3.14159 are decimal numerals. |
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The number of digits in the fractional part is sometimes called the ''accuracy'' of the decimal numeral. The [[subtraction|difference]] of two consecutive decimal numbers of {{nowrap|accuracy {{math|''n''}}}} is {{math|1/10<sup>''n''</sup>}}. This implies that every [[real number]] may be approximated to a decimal number of accuracy {{math|''n''}}, with an error, which is at most {{sfrac|1|2×10<sup>''n''</sup>}}. For this reason, decimal numeral are widely used in all [[science]] for representing any measurable quantity. |
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[[category:Elementary arithmetic]] |
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[[category:Positional numeral systems]] |
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Revision as of 17:55, 6 August 2017
A decimal number is a number that becomes an integer, when multiplied by a sufficiently high power of 10. A decimal numeral is the standard representation of a decimal number in the Hindu-Arabic numeral. A decimal numeral consists of a (finite) sequence of decimal digits representing an integer (the integer part), followed by a decimal mark (either dot "." or comma ",", depending on the country), and another finite sequence of digits, the fractional part. For representing integers, either the decimal mark and the fractional part are lacking, or the fractional part consists of one or several 0. For example, 32, 32.00, 3.14159 are decimal numerals.
The number of digits in the fractional part is sometimes called the accuracy of the decimal numeral. The difference of two consecutive decimal numbers of accuracy n is 1/10n. This implies that every real number may be approximated to a decimal number of accuracy n, with an error, which is at most 1/2×10n. For this reason, decimal numeral are widely used in all science for representing any measurable quantity.