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  2. Rounding - Wikipedia

    en.wikipedia.org/wiki/Rounding

    In a guideline issued in mid-1966, [49] the U.S. Office of the Federal Coordinator for Meteorology determined that weather data should be rounded to the nearest round number, with the "round half up" tie-breaking rule. For example, 1.5 rounded to integer should become 2, and −1.5 should become −1.

  3. Round-off error - Wikipedia

    en.wikipedia.org/wiki/Round-off_error

    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 to 0) is used. For IEEE standard where the base is , this means when there is a tie it is rounded so that the last digit is equal to .

  4. Python (programming language) - Wikipedia

    en.wikipedia.org/wiki/Python_(programming_language)

    Python provides a round function for rounding a float to the nearest integer. For tie-breaking , Python 3 uses round to even : round(1.5) and round(2.5) both produce 2 . [ 123 ] Versions before 3 used round-away-from-zero : round(0.5) is 1.0 , round(-0.5) is −1.0 .

  5. Machine epsilon - Wikipedia

    en.wikipedia.org/wiki/Machine_epsilon

    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.

  6. Unit in the last place - Wikipedia

    en.wikipedia.org/wiki/Unit_in_the_last_place

    Here we start with 0 in single precision (binary32) and repeatedly add 1 until the operation does not change the value. Since the significand for a single-precision number contains 24 bits, the first integer that is not exactly representable is 2 24 +1, and this value rounds to 2 24 in round to nearest, ties to even.

  7. Floating-point arithmetic - Wikipedia

    en.wikipedia.org/wiki/Floating-point_arithmetic

    It is used to round the 33-bit approximation to the nearest 24-bit number (there are specific rules for halfway values, which is not the case here). This bit, which is 1 in this example, is added to the integer formed by the leftmost 24 bits, yielding: 11001001 00001111 1101101 1 _ . {\displaystyle 11001001\ 00001111\ 1101101{\underline {1}}.}

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    mail.aol.com/?rp=webmail-std/en-us/basic

    Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!

  9. IEEE 754 - Wikipedia

    en.wikipedia.org/wiki/IEEE_754

    Round to nearest, ties to even – rounds to the nearest value; if the number falls midway, it is rounded to the nearest value with an even least significant digit. Round to nearest, ties away from zero (or ties to away ) – rounds to the nearest value; if the number falls midway, it is rounded to the nearest value above (for positive numbers ...