# Round a Python list of numbers and maintain their sum

I have a list or an array of decimal numbers in Python. I need to round them to the nearest 2 decimal places as these are monetary amounts. But, I need the overall sum to be maintained, i.e. the sum of the original array rounded to 2 decimal places must be equal to the sum of the rounded elements of the array.

Here’s my code so far:

``````myOriginalList = [27226.94982, 193.0595233, 1764.3094, 12625.8607, 26714.67907, 18970.35388, 12725.41407, 23589.93271, 27948.40386, 23767.83261, 12449.81318]
originalTotal = round(sum(myOriginalList), 2)

# Using numpy
myRoundedList = numpy.array(myOriginalList).round(2)
# New Array = [ 27226.95    193.06   1764.31  12625.86  26714.68  18970.35  12725.41 23589.93 27948.4   23767.83  12449.81]

newTotal = myRoundedList.sum()
``````

I need an efficient way of amending my new rounded array such that the sum is also 187976.61. The 2 pence difference needs to be applied to items 7 and 6 as these have the greatest difference between the rounded entries and the original entries.

The first step is to calculate the error between the desired result and the actual sum:

``````>>> error = originalTotal - sum(myRoundedList)
>>> error
0.01999999996041879
``````

This can be either positive or negative. Since every item in `myRoundedList` is within 0.005 of the actual value, this error will be less than 0.01 per item of the original array. You can simply divide by 0.01 and round to get the number of items that must be adjusted:

``````>>> n = int(round(error / 0.01))
>>> n
2
``````

Now all that’s left is to select the items that should be adjusted. The optimal results come from adjusting those values that were closest to the boundary in the first place. You can find those by sorting by the difference between the original value and the rounded value.

``````>>> myNewList = myRoundedList[:]
>>> for _,i in sorted(((myOriginalList[i] - myRoundedList[i], i) for i in range(len(myOriginalList))), reverse=n>0)[:abs(n)]:
myNewList[i] += math.copysign(0.01, n)

>>> myRoundedList
[27226.95, 193.06, 1764.31, 12625.86, 26714.68, 18970.35, 12725.41, 23589.93, 27948.4, 23767.83, 12449.81]
>>> myNewList
[27226.95, 193.06, 1764.31, 12625.86, 26714.68, 18970.359999999997, 12725.42, 23589.93, 27948.4, 23767.83, 12449.81]
>>> sum(myNewList)
187976.61``````