Editing Rounding (section)

====Rounding half away from zero====
One may also '''round half away from zero''' (or '''round half toward infinity'''), a tie-breaking rule that is commonly taught and used, namely: If the fractional part of {{mvar|x}} is exactly 0.5, then {{math|1=''y'' = ''x'' + 0.5}} if {{mvar|x}} is positive, and {{math|1=''y'' = ''x'' − 0.5}} if {{mvar|x}} is negative.

: <math>
y = \sgn(x) \left\lfloor \left| x \right| + \tfrac12 \right\rfloor
= -\sgn(x) \left\lceil -\left| x \right| - \tfrac12 \right\rceil
= \begin{cases}
  \left\lfloor x + \tfrac12 \right\rfloor = \left\lceil \tfrac12 \lfloor 2x \rfloor \right\rceil & x \ge 0 \\[5mu]
  \left\lceil x - \tfrac12 \right\rceil = \left\lfloor \tfrac12 \lceil 2x \rceil \right\rfloor & x < 0
\end{cases}
</math>

For example, 23.5 gets rounded to 24, and −23.5 gets rounded to −24.

This can be more efficient on computers that use [[sign-magnitude]] representation for the values to be rounded, because only the first omitted digit needs to be considered to determine if it rounds up or down. This is one method used when rounding to [[significant figures]] due to its simplicity.

This method, also known as '''commercial rounding''',{{citation needed|date=November 2020}} treats positive and negative values symmetrically, and therefore is free of overall positive/negative bias if the original numbers are positive or negative with equal probability. It does, however, still have bias away from zero.

It is often used for currency conversions and price roundings (when the amount is first converted into the smallest significant subdivision of the currency, such as cents of a euro) as it is easy to explain by just considering the first fractional digit, independently of supplementary precision digits or sign of the amount (for strict equivalence between the paying and recipient of the amount).