# Scientific notation

5 messages
Open this post in threaded view
|
Report Content as Inappropriate

## Scientific notation

 The following multiple-choice item appeared in a campus-wide quiz in an Intermediate Algebra course.   Write in scientific notation: 255,000. (1)  255 x 10^3 (2) 25.5 x 10^4 (3) 2.55 x 10^5 (4) 255,000   When I expressed my opinion that the presumed correct answer (3) is incorrect as it doesn't preserve the precision implied by the original 255,000 , a fellow instructor asserted "Since 2.55 = 2.55000, I don't see anything wrong with our answers." Please help us clarify this matter.  Thank you in advance.   John Lee
Open this post in threaded view
|
Report Content as Inappropriate

## Re: Scientific notation

 I would say that in a mathematical sense, your friend is right. In a physical (measurement) sense, you are right. It is hard to talk about precision without some context. For example, 255,000 might only have 3 digits of precision. You really don't know how many digits of precision that number has because it wasn't indicated (which is an advantage of scientific notation). Generally, they would indicate the precision separately if they are just using standard notation. But you are correct to say that a number written as 2.55000 * 10^5 has 6 digits of precision. Anyways, that is how I would describe it.
Open this post in threaded view
|
Report Content as Inappropriate

## Re: Scientific notation

 In reply to this post by DCJLEE (3) is correct based on standard usage. Unless additional information is given, one should assume that the original number was only accurate to three significant digits. Including one or more zeros in the solution would indicate a level of accuracy that is not evident in the original. If the number of arose in integer-only arithmetic, or some such, scientific notation would be inappropriate because, even with the zeros, it would indicate an approximate real number, not an integer. Wayne At 02:38 AM 8/16/2009, [hidden email] wrote: > >The following multiple-choice item appeared in a campus-wide quiz in >an Intermediate Algebra course. > >Write in scientific notation: 255,000. >(1)  255 x 10^3 >(2) 25.5 x 10^4 >(3) 2.55 x 10^5 >(4) 255,000 > >When I expressed my opinion that the presumed correct answer (3) is >incorrect as it doesn't preserve the precision implied by the >original 255,000 , a fellow instructor asserted "Since 2.55 = >2.55000, I don't see anything wrong with our answers." Please help >us clarify this matter. >Thank you in advance. > >John Lee > > >---------- > > >__________ Information from ESET NOD32 Antivirus, version of virus >signature database 4340 (20090816) __________ > >The message was checked by ESET NOD32 Antivirus. > >http://www.eset.com
Open this post in threaded view
|
Report Content as Inappropriate

## Re: Scientific notation

 In reply to this post by DCJLEE John Lee wrote: http://mathforum.org/kb/message.jspa?messageID=6816836> The following multiple-choice item appeared in a campus-wide > quiz in an Intermediate Algebra course. > > Write in scientific notation: 255,000. > (1) 255 x 10^3 > (2) 25.5 x 10^4 > (3) 2.55 x 10^5 > (4) 255,000 > > When I expressed my opinion that the presumed correct > answer (3) is incorrect as it doesn't preserve the > precision implied by the original 255,000 , a fellow > instructor asserted "Since 2.55 = 2.55000, I don't see > anything wrong with our answers." Please help us clarify > this matter. > Thank you in advance. In my opinion, this is the kind of question that should be avoided in tests. If it is important for the student to know what "scientific notation" means, then it shouldn't be tested in a multiple choice format. It should be in a fill-in-the-blank format (which should be very easy to grade). It's also difficult for me to determine what is being tested, aside from simply knowing the meaning of a certain word, which to me isn't something that I'd consider all that important when making placement decisions or whatever the purpose of the test was. I'd be more interested in knowing whether the student could select the correct value of an expression such as [(3.6 x 10^5)(4 x 10^7)]  / [(6 x 10^3)(0.04 x 10^5)] (without a calculator, of course) or put into numerical order several values written in scientific notation or something else that actually tested mathematics. Dave L. Renfro