piclist 2001\05\31\133343a >
www.piclist.com/techref/index.htm?key=brain+burp+rounding
BY : Paul Hutchinson email (remove spam text)

>No, actually 4.99999999999 (repeating) is the half-way point.
>5.0 is definitely in the top half.

4.99999999999 (repeating) = 5.00000000 (repeating)
Remember, repeating decimals are equal to an integer divided by 9.
1/9 = 0.1(repeating)
2/9 = 0.2(repeating)
3/9 = 0.3(repeating) = 1/3
4/9 = 0.4(repeating)
5/9 = 0.2(repeating)
6/9 = 0.6(repeating) = 2/3
7/9 = 0.7(repeating)
8/9 = 0.8(repeating)
9/9 = 0.9(repeating) = 1

Maybe this example will help illustrate the bias in >=5 rounding versus
odd/even rounding.

You have four numbers to sum, 1.5, 2.5, 3.5, 4.5
Using the decimal values:
1.5 + 2.5 + 3.5 + 4.5 = 12.

If we round using >=5 rounding:
2 + 3 + 4 + 5 = 14

If we round using odd/even rounding:
2 + 2 + 4 + 4 = 12

Is it any wonder that on Massachusetts State Income Taxes you must (by law)
use the >=5 rounding method, more revenue for the state :-).
Actually, because you use the same rounding for exemptions/deductions as for
income the revenue isn't any better for the state but, the simpler >=5
rounding is easier on the tax preparer.

BTW - The CINT() rounding function in all flavors of Microsoft Basic
languages uses odd/even rounding.

Paul

=========================================
Paul Hutchinson
Chief Engineer
Maximum Inc., 30 Samuel Barnet Blvd.
New Bedford, MA 02745
phutchinsonimtra.com
http://www.maximum-inc.com
=========================================

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