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(also written as 0. 9, 0.., or 0.(9)) is a repeating decimal that is an alternative way of writing the number 1. Following the standard rules for representing numbers in decimal notation, its value is the smallest number greater than or equal to every number in the sequence 0.9, 0.99, 0.999, ... .
In order to convert a rational number represented as a fraction into decimal form, one may use long division. For example, consider the rational number 5 / 74 : 0.0 675 74 ) 5.00000 4.44 560 518 420 370 500 etc. Observe that at each step we have a remainder; the successive remainders displayed above are 56, 42, 50.
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; for example: 9 1/2; 9 + 1 ⁄ 2 9 + 1 / 2
The hands value has at most one digit after the decimal mark, and has an optional fraction. A precision of 2 assumes |frac=2 (round to nearest 1 ⁄ 2 inch). A precision of 3 or more assumes |frac=4 (round to nearest 1 ⁄ 4 inch).
All the values of x begin at the 15 th decimal, so Excel must take them into account. Before calculating the sum 1 + x , Excel first approximates x as a binary number. If this binary version of x is a simple power of 2, the 15 digit decimal approximation to x is stored in the sum, and the top two examples of the figure indicate recovery of x ...
The fraction 0.538 falls into the sub-interval for NEUTRAL, [0, 0.6); this indicates that the first symbol the encoder read must have been NEUTRAL, so this is the first symbol of the message. Next divide the interval [0, 0.6) into sub-intervals: the interval for NEUTRAL would be [0, 0.36), 60% of [0, 0.6).
Some balanced ternary fractions have multiple representations too. For example, 1 / 6 = 0.1 𝖳 bal3 = 0.0 1 bal3. Certainly, in the decimal and binary, we may omit the rightmost trailing infinite 0s after the radix point and gain a representations of integer or terminating fraction.
Fractions such as 1 ⁄ 3 are displayed as decimal approximations, for example rounded to 0.33333333. 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.