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This variant of the round-to-nearest method is also called convergent rounding, statistician's rounding, Dutch rounding, Gaussian rounding, odd–even rounding, [6] or bankers' rounding. [ 7 ] This is the default rounding mode used in IEEE 754 operations for results in binary floating-point formats.
The nearest floating-point number with only five digits is 12.346. And 1/3 = 0.3333… is not a floating-point number in base ten with any finite number of digits. In practice, most floating-point systems use base two, though base ten (decimal floating point) is also common.
There are two common rounding rules, round-by-chop and round-to-nearest. The IEEE standard uses round-to-nearest. 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 ...
Suppose a person uses a scale that has a precision of one kilogram, where intermediate values cannot be discerned, and the true weight is rounded to the nearest whole number. For example, 79.6 kg and 80.3 kg are indistinguishable, as the scale can only display values to the nearest kilogram.
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 ...
The IEEE 754 standard defines precision as the number of digits available to represent real numbers. A programming language can include single precision (32 bits), double precision (64 bits), and quadruple precision (128 bits).
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[1] [2] More generally, divisor methods are used to round shares of a total to a fraction with a fixed denominator (e.g. percentage points, which must add up to 100). [2] The methods aim to treat voters equally by ensuring legislators represent an equal number of voters by ensuring every party has the same seats-to-votes ratio (or divisor).