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Excel maintains 15 figures in its numbers, but they are not always accurate; mathematically, the bottom line should be the same as the top line, in 'fp-math' the step '1 + 1/9000' leads to a rounding up as the first bit of the 14 bit tail '10111000110010' of the mantissa falling off the table when adding 1 is a '1', this up-rounding is not undone when subtracting the 1 again, since there is no ...
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.
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 .
A round number is an integer that ends with one or more "0"s (zero-digit) in a given base. [1] So, 590 is rounder than 592, but 590 is less round than 600. In both technical and informal language, a round number is often interpreted to stand for a value or values near to the nominal value expressed.
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 ...
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round to nearest, where ties round to the nearest even digit in the required position (the default and by far the most common mode) round to nearest, where ties round away from zero (optional for binary floating-point and commonly used in decimal) round up (toward +∞; negative results thus round toward zero)
Given real numbers x and y, integers m and n and the set of integers, floor and ceiling may be defined by the equations ⌊ ⌋ = {}, ⌈ ⌉ = {}. Since there is exactly one integer in a half-open interval of length one, for any real number x, there are unique integers m and n satisfying the equation