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All others are rounded to the closest integer. Whenever the fractional part is 0.5, alternate rounding up or down: for the first occurrence of a 0.5 fractional part, round up, for the second occurrence, round down, and so on. Alternatively, the first 0.5 fractional part rounding can be determined by a random seed. "Up" and "down" can be any two ...
Integral part: if x is a real number, [] often denotes the integral part or truncation of x, that is, the integer obtained by removing all digits after the decimal mark. This notation has also been used for other variants of floor and ceiling functions .
If it is converted to the centimeter scale and the rounding guideline for multiplication and division is followed, then 2 0.32 cm ≈ 20 cm with the implied uncertainty of ± 5 cm. If this implied uncertainty is considered as too overestimated, then more proper significant digits in the unit conversion result may be 2 0 .32 cm ≈ 20. cm with ...
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This alternative definition is significantly more widespread: machine epsilon is the difference between 1 and the next larger floating point number.This definition is used in language constants in Ada, C, C++, Fortran, MATLAB, Mathematica, Octave, Pascal, Python and Rust etc., and defined in textbooks like «Numerical Recipes» by Press et al.
Round-by-chop: The base-expansion of is truncated after the ()-th digit. This rounding rule is biased because it always moves the result toward zero. Round-to-nearest: () is set to the nearest floating-point number to . When there is a tie, the floating-point number whose last stored digit is even (also, the last digit, in binary form, is equal ...
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