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For instance, for units of length, a foot is 1/3 of a yard, and an inch is 1/12 of a foot, so a quantity of 5 yards, 2 feet, and inches could be represented as a composite fraction: yards. However, typical notations for traditional measures, while similarly based on mixed radixes, do not write out the denominators explicitly; the explicit ...
Stevin, however, did not use the notation we use today. He drew circles around the exponents of the powers of one tenth: thus he wrote 7.3486 as 7 3 (1) 4 (2) 8 (3) 6 (4). In De Thiende Stevin not only demonstrated how decimal fractions could be used but also advocated that a decimal system should be used for weights and measures and for coinage."
A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...
5.3 Fractions, matrices, multilines. ... Download as PDF; Printable version; In other projects ... installed on your system.
The Mathematical Treatise of Sunzi used decimal fraction metrology. The unit of length was 1 chi, 1 chi = 10 cun, 1 cun = 10 fen, 1 fen = 10 li, 1 li = 10 hao, 10 hao = 1 shi, 1 shi = 10 hu. 1 chi 2 cun 3 fen 4 li 5 hao 6 shi 7 hu is laid out on counting board as where is the unit measurement chi.
To determine the actual value, a decimal point is placed after the first digit of the significand and the result is multiplied by 10 5 to give 1.528535047 × 10 5, or 152,853.5047. In storing such a number, the base (10) need not be stored, since it will be the same for the entire range of supported numbers, and can thus be inferred.
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An example of a fraction that cannot be represented by a decimal expression (with a finite number of digits) is 1 / 3 , 3 not being a power of 10. More generally, a decimal with n digits after the separator (a point or comma) represents the fraction with denominator 10 n , whose numerator is the integer obtained by removing the separator.
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