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- 9)." Thanks! Debbie
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 http://mathforum.org/dr.math/problems/slaber.6.13.99.html and in this site linked in our Ask Dr. Math Rounding FAQ (http://mathforum.org/dr.math/faq/faq.rounding.html ): Rules for Rounding Numbers http://www.uop.edu/cop/psychology/Statistics/Rounding.html 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 http://mathforum.org/dr.math/
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 75.4."). 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
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