algorithm - How to make rounded percentages add up to 100%

Question

Consider the four percentages below, represented as float numbers:

    13.626332%
    47.989636%
     9.596008%
    28.788024%
   -----------
   100.000000%

I need to represent these percentages as whole numbers. If I simply use Math.round(), I end up with a total of 101%.

14 + 48 + 10 + 29 = 101

If I use parseInt(), I end up with a total of 97%.

13 + 47 + 9 + 28 = 97

What's a good algorithm to represent any number of percentages as whole numbers while still maintaining a total of 100%?

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Edit: After reading some of the comments and answers, there are clearly many ways to go about solving this.

In my mind, to remain true to the numbers, the "right" result is the one that minimizes the overall error, defined by how much error rounding would introduce relative to the actual value:

        value  rounded     error               decision
   ----------------------------------------------------
    13.626332       14      2.7%          round up (14)
    47.989636       48      0.0%          round up (48)
     9.596008       10      4.0%    don't round up  (9)
    28.788024       29      2.7%          round up (29)

In case of a tie (3.33, 3.33, 3.33) an arbitrary decision can be made (e.g. 3, 4, 3).

Answer 1

There are many ways to do just this, provided you are not concerned about reliance on the original decimal data.

The first and perhaps most popular method would be the Largest Remainder Method

Which is basically:

1. Rounding everything down
2. Getting the difference in sum and 100
3. Distributing the difference by adding 1 to items in decreasing order of their decimal parts

In your case, it would go like this:

13.626332%
47.989636%
 9.596008%
28.788024%

If you take the integer parts, you get

13
47
 9
28

which adds up to 97, and you want to add three more. Now, you look at the decimal parts, which are

.626332%
.989636%
.596008%
.788024%

and take the largest ones until the total reaches 100. So you would get:

14
48
 9
29

Alternatively, you can simply choose to show one decimal place instead of integer values. So the numbers would be 48.3 and 23.9 etc. This would drop the variance from 100 by a lot.