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Topic: A2/TrigRegentsReview
Replies: 10   Last Post: Jun 19, 2012 10:45 AM

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Evan Romer

Posts: 168
Registered: 1/8/09
Re: decimal question on Regents
Posted: Jun 18, 2012 11:52 PM
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I teach Precalc, and I've always told my students not to write down
intermediate results and re-enter them but to use ANS or memory
instead. The reason (aside from saving time and not making typing
errors) is that while the calculator shows you 10 digits of accuracy,
it stores the number internally with 14 digits of accuracy. When you
use ANS or memory it uses the 14-digit number. (And, for other
reasons, I want them to get comfortable using memory.)

Now that the TI-84s have the up-arrow trick, the same applies: when
you use the up-arrow to copy a previous result, it only copies the
visible digits, so you lose accuracy.

Having said that, I can't see why anyone would take off points on the
Regents for an answer that is wrong in the 8th decimal place.

Evan Romer
Susquehanna Valley HS
Conklin NY

P.S. To see this about accuracy, type 1/7: you get 10 digits of
accuracy. Now subtract 0.14. Now multiply by 100: suddenly you have
more digits that it must have been hiding from you. Do it again:
subtract 0.28, multiply by 100 -- more digits. Again: subtract 0.57
and multiply by 100 -- now we don't get any more digits :( So it
must have calculated 1/7 to 14 decimal places.

P.P.S. A simpler example than e^ln 8 (accessible to younger students)
to convince students that the up-arrow trick is inaccurate. Find
sqrt(6), then compare (a) ANS^2, (b) storing in memory and then
squaring, and (c) copy-by-up-arrow and square. You get (a) 6 (b) 6 (c)
6.000000001. For further discussion, you might note that even in (a)
and (b), since the calculator does not find sqrt(6) with an infinite
number of decimals, when you square ANS the calculator must not
actually get 6. It gets "close enough" to 6, and then I think TI
cheats and makes the answer 6.

On Jun 18, 2012, at 8:52PM, Eleanor Pupko wrote:

> 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).
> Thanks,
> Eleanor Pupko

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