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### Rounding Logic

```
Date: 12/11/96 at 00:40:34
From: Mason
Subject: Rounding

Dr. Math,

Who invented the fact that when you have 5,50,500,5000, etc. you
always round UP, instead of down?

Mason
```

```
Date: 12/11/96 at 11:26:20
From: Doctor Rob
Subject: Re: Rounding

I haven't any idea why you round up, but there is a certain logic
to it (although I'm not sure I agree with the results!).  Consider
numbers like 73.0, 73.1, 73.2, 73.3, 73.4, 73.5, 73.6, 73.7, 73.8,
73.9 just for the sake of this argument. Say we want to round them
off to whole numbers. In an effort to be accurate, it is clear you
should round down the first five and round up the last four. It is
only the sixth number that leaves us in a bit of a pickle. It seems
only fair/logical that if we round five cases down, we should
round five cases up, too, rather than split the cases into six up and
only four down. So maybe that's why it's the way that it is.

It's also very important to have everyone who does math do the same
thing so that their answers agree.  We'd all be confused if some
people rounded 550 up to 600 and others rounded it down to 500.
That's a pretty big difference in results!  Math is filled with lots
of cases like this (they're called conventions) that you just have to
follow so that we can talk to each other without being confused.

-Doctor Rob,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Fractions
Elementary Place Value

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