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In the rare case that these other methods all fail, Fibonacci suggests a "greedy" algorithm for computing Egyptian fractions, in which one repeatedly chooses the unit fraction with the smallest denominator that is no larger than the remaining fraction to be expanded: that is, in more modern notation, we replace a fraction x / y by the ...
In mathematics a rational number is a number that can be represented by a fraction of the form ... can be expanded as an Egyptian fraction. ... 5 / 10 = 1 ...
10/5 may refer to: October 5 (month-day date notation) May 10 (day-month date notation) 10 shillings and 5 pence in UK predecimal currency; See also.
Al Khwarizmi introduced fractions to Islamic countries in the early 9th century; his fraction presentation was similar to the traditional Chinese mathematical fractions from Sunzi Suanjing. [10] This form of fraction with numerator on top and denominator at bottom without a horizontal bar was also used by 10th century Abu'l-Hasan al-Uqlidisi ...
123.45 = 12345 × 10 −2. This same value can also be represented in scientific notation with the significand 1.2345 as a fractional coefficient, and +2 as the exponent (and 10 as the base): 123.45 = 1.2345 × 10 +2. Schmid, however, called this representation with a significand ranging between 1.0 and 10 a modified normalized form. [12] [13]
Every terminating decimal representation can be written as a decimal fraction, a fraction whose denominator is a power of 10 (e.g. 1.585 = 1585 / 1000 ); it may also be written as a ratio of the form k / 2 n ·5 m (e.g. 1.585 = 317 / 2 3 ·5 2 ).
This "over" form is also widely used in mathematics. Fractions together with an integer are read as follows: 1 + 1 ⁄ 2 is "one and a half" 6 + 1 ⁄ 4 is "six and a quarter" 7 + 5 ⁄ 8 is "seven and five eighths" A space is placed to mark the boundary between the whole number and the fraction part unless superscripts and subscripts are used ...
Henri Padé further expanded this notion in his doctoral thesis Sur la representation approchee d'une fonction par des fractions rationelles, in 1892. Over the ensuing 16 years Padé published 28 additional papers exploring the properties of his table, and relating the table to analytic continued fractions. [1]