Why does Math.Round(2.5) return 2 instead of 3?

Question

In C#, the result of Math.Round(2.5) is 2.

It is supposed to be 3, isn\'t it? Why is it 2 instead in C#?

Answer 1

The nature of rounding

Consider the task of rounding a number that contains a fraction to, say, a whole number. The process of rounding in this circumstance is to determine which whole number best represents the number you are rounding.

In common, or 'arithmetic' rounding, it is clear that 2.1, 2.2, 2.3 and 2.4 round to 2.0; and 2.6, 2.7, 2.8 and 2.9 to 3.0.

That leaves 2.5, which is no nearer to 2.0 than it is to 3.0. It is up to you to choose between 2.0 and 3.0, either would be equally valid.

For minus numbers, -2.1, -2.2, -2.3 and -2.4, would become -2.0; and -2.6, 2.7, 2.8 and 2.9 would become -3.0 under arithmetic rounding.

For -2.5 a choice is needed between -2.0 and -3.0.

Other forms of rounding

'Rounding up' takes any number with decimal places and makes it the next 'whole' number. Thus not only do 2.5 and 2.6 round to 3.0, but so do 2.1 and 2.2.

Rounding up moves both positive and negative numbers away from zero. Eg. 2.5 to 3.0 and -2.5 to -3.0.

'Rounding down' truncates numbers by chopping off unwanted digits. This has the effect of moving numbers towards zero. Eg. 2.5 to 2.0 and -2.5 to -2.0

In "banker's rounding" - in its most common form - the .5 to be rounded is rounded either up or down so that the result of the rounding is always an even number. Thus 2.5 rounds to 2.0, 3.5 to 4.0, 4.5 to 4.0, 5.5 to 6.0, and so on.

'Alternate rounding' alternates the process for any .5 between rounding down and rounding up.

'Random rounding' rounds a .5 up or down on an entirely random basis.

Symmetry and asymmetry

A rounding function is said to be 'symmetric' if it either rounds all numbers away from zero or rounds all numbers towards zero.

A function is 'asymmetric' if rounds positive numbers towards zero and negative numbers away from zero.. Eg. 2.5 to 2.0; and -2.5 to -3.0.

Also asymmetric is a function that rounds positive numbers away from zero and negative numbers towards zero. Eg. 2.5 to 3.0; and -2.5 to -2.0.

Most of time people think of symmetric rounding, where -2.5 will be rounded towards -3.0 and 3.5 will be rounded towards 4.0. (in C# Round(AwayFromZero))