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Reading with interest the conversation on sig figs and rounding. A couple of years ago I was struggling with students not knowing how to round numbers. To my surprise, I wasn't rounding correctly either! See the following from a math web site (citation lost in the mists of time). Does anyone use this method?
When rounding, examine the figure following (i.e., to the right of) the figure that is to be last. This figure you are examining is the first figure to be dropped.
If it is less than 5, drop it and all the figures to the right of it.
If it is more than 5, increase by 1 the number to be rounded, that is, the preceding figure.
If it is 5, round the number so that it will be even. Keep in mind that zero is considered to be even when rounding off.
Example #1 - Suppose you wish to round 62.5347 to four significant figures. Look at the fifth figure. It is a 4, a number less than 5. Therefore, you will simply drop every figure after the fourth, and the original number rounds off to 62.53.
Example #2 - Round 3.78721 to three significant figures. Look at the fourth figure. It is 7, a number greater than 5, so you round the original number up to 3.79.
Example #3 - Round 726.835 to five significant figures. Look at the sixth figure. It is a 5, so now you must look at the fifth figure also. That is a 3, which is an odd number, so you round the original number up to 726.84.
Example #4 - Round 24.8514 to three significant figures. Look at the fourth figure. It is a 5, so now you must also look at the third figure. It is 8, an even number, so you simply drop the 5 and the figures that follow it. The original number becomes 24.8.
When the value you intend to round off is a five, you MUST look at the previous value ALSO. If it is even, you round down. If it is odd, you round up. A common question is "Is zero considered odd or even?" The answer is even.
Original excel rules
0.5 1 0
1.5 2 2
2.5 3 2
3.5 4 4
4.5 5 4
5.5 6 6
6.5 7 6
7.5 8 8
8.5 9 8
9.5 10 10
William R. Wolowich, Pharm.D, R.Ph.
Chair, Department of Pharmacy Practice
College of Pharmacy
Nova Southeastern University
[Ansel and Stoklosa, Pharmaceutical Calculations, 12th edition, p20 has rounding rules, #2 -- add 1 to last figure retained if figure to be dropped is 5 or above. No mention of odd/even.
Googling gave one reference that calls the method presented above as the "Banker's Rule" ;-)
Wikipedia gives quite a collection of methods under the heading "Tie-breaking" see http://en.wikipedia.org/wiki/Rounding
As a Pharmacy Math instructor I find the students have more problems with the related subject of significant figures with numbers above and below 1 - db]
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The following message was posted to: PharmPK
Dr. Wolowich has described one particular rule relevant to rounding the value 5. He has selected the "round 5 to even" rule. But, there are other approaches and one needs to be aware of which one is being implemented by particular software:
Excel - rounds up.
R - rounds to even
Wikipedia -- http://en.wikipedia.org/wiki/Rounding#Round_half_up -- provides a list of a number of other methods.
Dennis Fisher MD
P < (The "P Less Than" Company)
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