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Rounding Decimals: Even/Odd Issues

Date: 05/08/2001 at 11:36:53
From: Deborah Dann
Subject: Rounding decimals

This is a strange question... I remember learning a way to round 
certain numbers, but now I think I am going crazy!  Please help - 
here is what I remember:

When an even decimal (or any even number) is followed by a 5, you 
round down. When an odd decimal is followed by a 5, you round up.  
For example: 75.45 = 75.4, but 75.55=75.6. Or rounding to the nearest 
10: 145 = 140, but 155 = 160.

Can you let me know if I learned the "rule" incorrectly?  It seemed 
from the info on your page, I did learn it incorrectly; but it has 
persisted in my memory!  As you've said on your page, statistically 
we should "round down the first 5 (1-4) and round up the last 5 (5-


Date: 05/08/2001 at 13:11:26
From: Doctor Peterson
Subject: Re: Rounding decimals

Hi, Debbie.

There are two ways to round that are commonly taught. The rules we 
give in most of our answers are those taught to children (and commonly 
used by computers), because they are simpler but are sufficient for 
most purposes. Where statistics matter, and where numbers that END 
with the 5 are common, the method you referred to is preferred, 
because it avoids a bias toward rounding up. On the other hand, there 
may be some situations where a bias toward numbers that end in an even 
digit might be bad. Each method has its place.

You can read a little about this here:

   Rounding Up or Down on a 5   

and in this site linked in our Ask Dr. Math Rounding FAQ
(   ):

   Rules for Rounding Numbers   

One aspect of this improved rule that can be easily missed is that you 
only look at the even/odd issue when the number you are rounding is 
EXACTLY halfway; for example, you wouldn't round 75.451 down to 75.4, 
because there is another digit beyond the 5, and 75.451 is closer to 
75.5 than to 75.4. The other method only requires you to look at the 
first digit being dropped, regardless of whether there are any digits 
following it.

- Doctor Peterson, The Math Forum   

Date: 05/08/2001 at 14:01:39
From: Dann, Deborah
Subject: Re: Rounding decimals

Dr. Peterson, 

Thanks very much! Now I know I've not gone completely nuts! But the 
caveat you suggest is one I do overlook, and should be considered 
("for example, you wouldn't round 75.451 down to 75.4, because there 
is another digit beyond the 5, and 75.451 is closer to 75.5 than to 

And thanks for replying so quickly.  I've bookmarked your page - even 
though I teach college students, sometimes they need to be reminded of 
stuff they already learned!

Deborah M. Dann
Instructor of Astronomy and Geology
Corning Community College
Associated Topics:
Elementary Fractions
Elementary Place Value

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