I am trying to answer the question whether:
Round(a + b + c) = Round(a) + Round(b) + Round(c)
(Forgive me if "distributive" is the wrong term, been some time since my math days)
Context:
I have financial transactions data in which each amount is written in cents. Due to historical error, some of the amounts had 2 numbers after the decimal points (for example 300.02 cents which is $3.0002).
At the end of each month, we would sum up all transactions and round the result. I want to fix the historical error so that I only have integers in my data and I was wondering if the results with bad data (after rounding) would still equal the results with fixed data.
Thanks!
No. Let a = b = c = 1.2 Then Round$(1.2+1.2+1.2)$ = Round$(3.6)=4$, but $3$Round$(1.2)=3.$ Generally, you should always round after the calculations are done, if possible.