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### Rounding to the Nearest Multiple of 5

```Date: 01/08/2005 at 00:30:11
From: Jim
Subject: Rounding

How do you round to the nearest 5's?  Let's say you have the numbers
22, 27, or 28.  Would the 22 round down to 20, also would the 27 round
down to 25?  And would 28 round up to 30?

I personally do not find anything difficult about it.  I may be wrong,
but simple logic tells me that 22 and 27 would round down and 28 up.
A couple of acquaintances of mine disagree with me about rounding down
the number 27.

My logic is that the numbers 1, 2, 6, 7 and any numbers ending with
these digits, i.e 11, 22, 31, 56, 67 and 82, when rounding to the
nearest 5's would round down.  As where the numbers 3, 4, 8 and 9 and
any other respective numbers ending in these digits would round up.

```

```
Date: 01/08/2005 at 23:00:26
From: Doctor Peterson
Subject: Re: Rounding

Hi, Jim.

You're essentially right, though you haven't completely spelled out
the rule.  The main idea is that you want to literally find the
nearest multiple of 5 to the given number, so all you really have to
do is to find the two nearest multiples of 5, and then see which is
nearer.  For example, take 27.  It lies between 25 and 30; it is 2
away from 25 and 3 away from 30, so 25 is nearer.  Case closed.

One way to do this rounding is to just round down anything less than
2.5 above the lower multiple of 5, and round up anything greater than
2.5 above it.  Another way to do it is to divide by 5, round to the
nearest whole number, and then multiply by 5 again.  For 27, dividing
by 5 gives 5.4, rounding gives 5, and multiplying takes us to 25 as
before.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
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