Subtleties of Rounding
Date: 09/24/2003 at 13:05:43 From: John Subject: Rounding decimals There are 480 freshmen at Washington High. If 36% of the freshmen play sports, how many play sports? Is the correct answer 172 or 173? The argument for 172 is that you cannot have .8 of a person so you round down to 172. The argument for 173 is that you should round to the nearest whole number (and that 173 is closer to 36% of 480 than 172 is).
Date: 09/24/2003 at 14:55:18 From: Doctor Peterson Subject: Re: Rounding decimals Hi, John. I think rounding to 173 is best if you need a specific answer; but in reality we don't quite know. If someone who knew the actual number calculated the percentage to the nearest percentage point, and told us that it is 36%, then the exact percentage might be anywhere from 35.5% to 36.5%, corresponding to numbers from 170.4 to 175.2. That means that the original number might have been 171, 172, 173, 174, or 175! In each of those cases, the percentage would come to 36% after rounding; so all are equally possible. If we take the given percentage as 36.0%, accurate to the nearest tenth of a percentage point, then there have to be 173 playing sports, since percentages of 35.95% and 36.05% correspond to 172.56 and 173.04. You can see why rounding to the nearest whole number makes sense. If we take the percentage as being _exactly_ 36%, of course, then somebody on the team is missing a few body parts. That's why we HAVE to make some assumption about the precision of the data. I love these little problems that turn out to be a lot more complicated than they seemed on the surface! 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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