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One method, more obscure than most, is to alternate direction when rounding a number with 0.5 fractional part. 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.
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 ...
Prices are rounded down to the nearest multiple of 5 cents for sales ending in 1¢ & 2¢ (rounded to 0¢) and 6¢ & 7¢ (rounded to 5¢). Prices are rounded up to the nearest multiple of 5 cents for sales ending in 3¢ & 4¢ (round to 5¢) and 8¢ & 9¢ (round to 10¢). Values ending in 0¢ or 5¢ remain unchanged.
Alternative rounding options are also available. IEEE 754 specifies the following rounding modes: 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 number bias is the psychological tendency to prefer round numbers over others, [4] [5] which is passed onto a person through socialization. [6] Round numbers are also easier for a person to remember, process, and perform mathematical operations on.
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Numbers with a magnitude strictly larger than k are rounded to the corresponding infinity. [18] "Round to nearest, ties to even" is the default for binary floating point and the recommended default for decimal. "Round to nearest, ties to away" is only required for decimal implementations. [19]
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