Rounding to a specified increment

The a lot of accepted blazon of rounding is to annular to an integer; or, added generally, to an accumulation assorted of some accession — such as rounding to accomplished tenths of seconds, hundredths of a dollar, to accomplished multiples of 1/2 or 1/8 inch, to accomplished dozens or thousands, etc..

In general, rounding a amount x to a assorted of some authentic accession m entails the afterward steps:

Divide x by m, let the aftereffect be y;

Round y to an accumulation value, alarm it q;

Multiply q by m to access the angled amount z.

For example, rounding x = 2.1784 dollars to accomplished cents (i.e., to a assorted of 0.01) entails accretion y = x/m = 2.1784/0.01 = 217.84, again rounding y to the accumulation q = 218, and assuredly accretion z = q×m = 218×0.01 = 2.18.

When rounding to a agreed amount of cogent digits, the accession m depends on the consequence of the amount to be angled (or of the angled result).

The accession m is commonly a bound atom in whatever amount arrangement that is acclimated to represent the numbers. For affectation to humans, that usually agency the decimal amount arrangement (that is, m is an accumulation times a ability of 10, like 1/1000 or 25/100). For average ethics stored in agenda computers, it generally agency the bifold amount arrangement (m is an accumulation times a ability of 2).

The abstruse single-argument "round()" action that allotment an accumulation from an approximate absolute amount has at atomic a dozen audible accurate definitions presented in the rounding to accumulation section. The abstruse two-argument "round()" action is formally authentic here, but in abounding cases it is acclimated with the absolute amount m = 1 for the accession and again reduces to the agnate abstruse single-argument function, with aswell the aforementioned dozen audible accurate definitions.