# Math question: what is half rounding?

#### Quattro Pete

Can you give me an example? Thanks.

#### Boomer

If you owe me 50 cents, I'll round it to a dollar. If I owe you a dollar, I'll round it down to zero. Half the time it goes one way, the other half the other!! Just kidding. I have no idea.

#### mechtech2

\$.49 or lower rounds to zero. \$.50 cents or higher rounds to \$1. Cash is ONE example.

#### moribundman

Originally Posted By: Quattro Pete
Can you give me an example? Thanks.
Half-rounding is about eliminating one decimal place. 9.0024 rounds to 9.002 9.0025 rounds to either 9.002 or 9.003 9.0026 rounds to 9.003

#### GROUCHO MARX

When I'm paying, I half round down. When I'm getting paid, I half round up.

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#### Quattro Pete

Originally Posted By: moribundman
Half-rounding is about eliminating one decimal place. 9.0024 rounds to 9.002 9.0025 rounds to either 9.002 or 9.003 9.0026 rounds to 9.003
OK, so what is the difference between half rounding and full rounding?

#### javacontour

Are you sure it's now how values such as 5.5 are handled? I've seen all sorts of different ways that such a value is handled and those are given different names such as round-half-even, round-half-odd, round-half-floor and so on. That has to do with how you are going to treat a value such as 5.5 when rounding to the nearest integer. I.E values such as 5.1, 5.2, 5.3 and 5.4 are all rounded to 5.0. Values such as 5.6, 5.7, 5.8, and 5.9 are all rounded to 6.0 But if you always round the 5.5 or 4.5 or 6.5 and so forth the same direction, you get more error introduced if there are more and more occasions where numbers are rounded. One can reduce this error by either randomly rounding the "halfs" up or down, or picking rules such as evens round up, odds round down. I.E. 5.5 rounds to 5.0 and 4.5 rounds to 5.0 So are you sure the question is not about all the different ways to treat 1/2 values?

#### moribundman

java, what you describe is the round-to-even rule, I think. As you have described, this method ideally reduces error accumulation when working with a number of rounded figures. Pete, I don't ever hear anybody talking about "full rounding," but the term "half rounding" does ring a (faint) bell.

#### Quattro Pete

Here's what I thought. Let me give my own examples. A. Full rounding: 1.2 rounds down to 1 1.4 rounds down to 1 1.6 rounds up to 2 1.8 rounds up to 2 B. Half rounding: 1.2 rounds down to 1 1.4 rounds up to 1.5 1.6 rounds down to 1.5 1.8 rounds up to 2 But from what you guys described, that is not the case.

#### javacontour

Originally Posted By: moribundman
java, what you describe is the round-to-even rule, I think. As you have described, this method ideally reduces error accumulation when working with a number of rounded figures. Pete, I don't ever hear anybody talking about "full rounding," but the term "half rounding" does ring a (faint) bell.
Yes, I gave one example of the different ways to treat 1/2 values. As indicated, there are others, such as always round up, always round down, odd rounding, and so on. I didn't even touch stochastic rounding, LOL.

#### moribundman

In B you are mixing "rounding to the next one" and "rounding to the next half," which are not mutually exclusive.

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