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Due to the use of fractions in many STV systems today, rounded-off variants of the Droop and Hagenbach-Bischoff quota may not be needed. The Britton or Newland-Britton quota [9] [a], sometimes called the "exact Droop" quota, is not rounded off and is slightly smaller than the Droop quota as Droop originally proposed it. Its formula is vote ...
The continued fraction representation for a real number is finite if and only if it is a rational number. In contrast, the decimal representation of a rational number may be finite, for example 137 / 1600 = 0.085625, or infinite with a repeating cycle, for example 4 / 27 = 0.148148148148...
For instance, the rational numbers , , and are written as 0.1, 3.71, and 0.0044 in the decimal fraction notation. [100] Modified versions of integer calculation methods like addition with carry and long multiplication can be applied to calculations with decimal fractions. [ 101 ]
The real-number Euclidean algorithm differs from its integer counterpart in two respects. First, the remainders r k are real numbers, although the quotients q k are integers as before. Second, the algorithm is not guaranteed to end in a finite number N of steps. If it does, the fraction a/b is a rational number, i.e., the ratio of two integers
For example, the decimal number 205 is the sum of two hundreds and five ones, with the 0 digit indicating that no tens are added. The digit plays the same role in decimal fractions and in the decimal representation of other real numbers (indicating whether any tenths, hundredths, thousandths, etc., are present) and in bases other than 10 (for ...
The seats-to-votes ratio for a political party is the ratio between the fraction of seats and the fraction of votes for that party: a i = s i v i {\displaystyle a_{i}={\frac {s_{i}}{v_{i}}}} The Sainte-Laguë method approximates proportionality by optimizing the seats-to-votes ratio among all parties i {\displaystyle i} with the least squares ...
The 680x0 line of processors has been used in a variety of systems, from high-end Texas Instruments calculators (the TI-89, TI-92, and Voyage 200 lines) to all of the members of the Palm Pilot series that run Palm OS 1.x to 4.x (OS 5.x is ARM-based), and even radiation-hardened versions in the critical control systems of the Space Shuttle.