Maybe I'm missing something here, but these examples merely demonstrate that if you use a rounded version of an irrational number in a future step, you may not (and most likely will not) get the desired answer. When one uses the "copy/paste" method of retrieving old values, you aren't retrieving the calculation that led to that value. You're only using the decimals that are displayed on the screen, which means that one must use the "ANS" command to retrieve the calculation to get the accurate result.
Steve Goldman Half Hollow Hills HS East Dix Hills, NY
-----Original Message----- From: Peggy Niforos <email@example.com> To: nyshsmath <firstname.lastname@example.org> Sent: Mon, Jun 18, 2012 11:50 pm Subject: RE: decimal question on Regents
I'm not sure what to say about the square root of 2 problem, but I always taught my students that calculator responses of things like 2.9999999999 or 8.000000003 meant that the calculator wants the answer to be 3 or 8. I teach them that technology has limitations and they have to use brain power every once in a while.
This applies to complex numbers in a large way. Technology is a tool and as such must be taught with the idea that it is not perfect. Peggy
From: email@example.com To: firstname.lastname@example.org Subject: RE: decimal question on Regents Date: Mon, 18 Jun 2012 20:52:32 -0400
How do you handle slight differences in a situation where, for example, a student graphs a parabola and the maximum function in the calculator gives x=2.999999999 but the answer is 3? The reason I am asking is because the new OS for the TI-84 gives two different answers depending on if you use the "2nd, ANS" feature versus the 'up-arrow and grab an answer'. I contend that if we expect students to use technology we should accept any answer obtained by using said technology. In this case the calculator is a TI-84, the OS has been approved and the APPS have been disabled for testing.
Some teachers are saying they will only accept one answer, ie 'their' answer. When I analyzed my students' exams last June I noticed that students lost points for answers that differed after 8 decimals due to this glitch in the new OS.
You can try the following if you have the 2.53 or 2.55 OS on your TI-84. If you take the square root of 2 ENTER and take the ln(up-arrow ENTER, ENTER you get an answer of .34657359. However, you take the square root of 2 ENTER and take the ln(2nd, Answer, ENTER you get .3465735903.
The second answer is the same as if you were to take the ln(square root of 2).
Another example involves e^(ln(8)). One method results in an answer of 8 and the other yields 8.00003 (don't have my calculator here to count the exact number of zeros but you get the idea).