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Any such decimal fraction, i.e.: d n = 0 for n > N, may be converted to its equivalent infinite decimal expansion by replacing d N by d N − 1 and replacing all subsequent 0s by 9s (see 0.999...). In summary, every real number that is not a decimal fraction has a unique infinite decimal expansion.
Also the converse is true: The decimal expansion of a rational number is either finite, or endlessly repeating. Finite decimal representations can also be seen as a special case of infinite repeating decimal representations. For example, 36 ⁄ 25 = 1.44 = 1.4400000...; the endlessly repeated sequence is the one-digit sequence "0".
The word mathematics comes from the Ancient Greek word máthēma (μάθημα), meaning ' something learned, knowledge, mathematics ', and the derived expression mathēmatikḗ tékhnē (μαθηματικὴ τέχνη), meaning ' mathematical science '. It entered the English language during the Late Middle English period through French and ...
Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one. Decimal representations are rounded or padded to 10 places if the values are known.
Also, some fractions (such as 1 ⁄ 7, which is 0.14285714285714; to 14 significant figures) can be difficult to recognize in decimal form; as a result, many scientific calculators are able to work in vulgar fractions or mixed numbers.
Any such symbol can be called a decimal mark, decimal marker, or decimal sign. Symbol-specific names are also used; decimal point and decimal comma refer to a dot (either baseline or middle ) and comma respectively, when it is used as a decimal separator; these are the usual terms used in English, [ 1 ] [ 2 ] [ 3 ] with the aforementioned ...
Decimal fractions are commonly expressed using decimal notation in which the implied denominator is determined by the number of digits to the right of a decimal separator, the appearance of which (e.g., a period, an interpunct (·), a comma) depends on the locale (for examples, see Decimal separator). Thus, for 0.75 the numerator is 75 and the ...