Why do we round up 0.5000 to 1 instead of rounding down to 0?
In: 12
.49999…., that is, .49 with 9 repeating forever, is exactly the same as 5. Infinity is weird.
.49999… rounds down.
5 rounds up.
We literally split five in half for this.
Granted, in practice, .49999…. is rare, while 5 is common. But it was as good of a reason as any for something that is completely arbitrary but had to be agreed upon in order for the community of mathematicians to work together.
Actually, we do! Sometimes. It’s a method called “Banker’s Rounding” (if memory serves), where 0.5 is rounded to the nearest even number. This balances out the rounding better.
There are many different ways of rounding. The one you mention is just the one most commonly taught in school. https://en.m.wikipedia.org/wiki/Rounding
1,2,3,4 round down
6,7,8,9 round up
So 5 could go either way. It is just typical convention to decide to round up. However, anything larger than 5 should round up, included if you have additional place values, so if 0.5000001 rounds up then it’s neater to do 5 and up with 5 inclusive than exclusive.
However, there are different conventions; for instance, “bankers rounding” alternates if 5 rounds up or down. Negatives also cause different conventions, some round -0.5 to -1 and other to 0.
There are many rounding methods to choose from and not just up or down. For school and lots of other common usages, the common way is just to round 0.5 to 1. It is arbitrary but it is what has been chosen.
The way you would round a number is not producing a half-up. What would you round -0.5 too, would it be 0 or -1? If the answer is zero you are not rounding up -1 is less than -0.5. 0.5 to 1 and -0.5 to -1 are rounding away from zero.
In some situations, a constant rounding away from zero results can be problematic. If you do not have an equal amount of negative and passive numbers the average rounding will change the result away from zero.
A way to help fix that is rounding half to even. So 0.5 become 1 but 3.5 become 3. That way if you just have a positive number that is event enough distributed the error is zero. It is still not preferred because the values you have might not be distributed like that.
The standard for computer floating point numbers (think decimal numbers) is to round to even. It is a binary fraction so not exactly rounding half but it is still an example of where rounding away from zero could introduce error and that is one way to reduce the error
https://en.wikipedia.org/wiki/Rounding
1,2,3,4 round down
6,7,8,9 round up
So 5 could go either way. It is just typical convention to decide to round up. However, anything larger than 5 should round up, included if you have additional place values, so if 0.5000001 rounds up then it’s neater to do 5 and up with 5 inclusive than exclusive.
However, there are different conventions; for instance, “bankers rounding” alternates if 5 rounds up or down. Negatives also cause different conventions, some round -0.5 to -1 and other to 0.
Well technically there are different rounding-modes to choose from.
But one has to be the default ….
Well technically there are different rounding-modes to choose from.
But one has to be the default ….
As others have mentioned, we don’t always round 0.5 up. There’s many different methods of rounding that are more appropriate for some applications than others, it just so happens that rounding 0.5 up is good enough for the vast majority of daily life applications.
There are 9 different numbers (0.1 – 0.9) that need rounding and only 2 options (0, 1) to chose from so it’s impossible to divide it evenly with a straight forward method so we had to randomly-ish chose one.
As others have mentioned, we don’t always round 0.5 up. There’s many different methods of rounding that are more appropriate for some applications than others, it just so happens that rounding 0.5 up is good enough for the vast majority of daily life applications.
There are 9 different numbers (0.1 – 0.9) that need rounding and only 2 options (0, 1) to chose from so it’s impossible to divide it evenly with a straight forward method so we had to randomly-ish chose one.
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