Rounding by a percent split

I need to round a number by a percentage split. but I need it to be a whole number and also add back up to the original number.

In the attached example, I am trying to split 160 by the percent Split Column (these percentages will change but will always add up to 100%)
I have shown 4 examples of the rounding available in Excel.

First one is with no rounding at all. All adds back up to 160. But I need it to round
Second one is the ROUND function. Adds up to 159
Third is the ROUNDUP function. Adds up to 164
And Fourth is ROUNDDOWN. Adds up to 158

What is the best rounding to get it back to its original figure?

By definition (Rounding to the nearest x or 0.1) is going to give you different numbers and thus a potentially different total.
What I would do, is take your largest percent (52) and instead (in your example), in D8

Formula:

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The result is actually 52.5% but close enough for government specs.

Reminds me of the true story of when (Feb 6, 1897) the legislature of Indiana tried to legally change the value of Pi to 3.2. Really, wanted to make it 3.2 officially, not just for business purposes, easy to remember, no more pesky infinite numbers. What's the harm? LOL

There may be better ways but here's what I did.
1. I inserted a blank row 10 between your values and totals (then made the row height small, you can hide instead)
2. In G3 copied down to G9

Formula:

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Please try this at H3

=ROUND(B3*$C$2,0)+(MATCH(1,FREQUENCY(0,1/(ABS($B$3:$B$9*$C$2-ROUND($B$3:$B$9*$C$2,0))*10^6+$B$3:$B$9)),)=ROWS(H$3:H3))*($C$2-SUM(ROUND($B$3:$B$9*$C$2,0)))