Hi!
i tried a simple calculation on 2 of my CASIO, the FX-602P and the fx-4000P.
i did just simply sqrt 2, and then ^2 of the result on both.
FX-602P :
sqrt 2 = 1.414213562
this result ^2 gives 2.
fx-4000P:
sqrt 2 = 1.414213562
this result ^2 gives 1.999999999
Anyone know why the FX-602P comes up with the correct answer 2,
and the fx-4000P not?
Maybe simple to explain, but i cant figure it out.
Both calculators evaluate results to 12 significant figures: \(\sqrt{2}\approx 1.414\,213\,562\,37\). Squaring this number gives 2, to 10 significant figures. This is what is displayed on the FX-602P.
However, pressing the EXE key on the FX-4000P rounds the result to 10 significant figures: \(\sqrt{2}\approx 1.414\,213\,562\). Squaring this rounded number gives \(1.999\,999\,999\), to 10 significant figures.
The rounding happens, I guess, because registers on the FX-4000P only store 10 significant figures. Pressing EXE stores the displayed number into the Ans register, hence the rounding. There is no Ans register on the FX-602P, and in any case the FX-602P's registers store all 12 digits of a calculated result.
Typing \((\sqrt{2})^2\) EXE on the FX-4000P gives an answer of 2, as the rounding doesn't occur until the calculation is complete.
Incidentally, the answer on the FX-602P is not exactly correct. Squaring \(1.414\,213\,562\,37\) gives \(1.999\,999\,999\,99\), rounded to 12 significant figures. The FX-602P rounds the answer to 2, exactly. Quite a lot of Casio calculators do this - personally, I disapprove!
Nigel (UK)
wow, that was a great explanation!
I had no idea of this.
So, the old FX-602P handles this much better than the newer
fx-4000P then.
Thank you! I agree: in this respect, the FX-602P is definitely the better of the two. Still, the FX-4000P wins on built-in functions!
Nigel (UK)
(10-27-2021 04:23 PM)Dan C Wrote: [ -> ]Anyone know why the FX-602P comes up with the correct answer 2,
and the fx-4000P not? Maybe simple to explain, but i cant figure it out.
Hi, it was earlier; check the page 62 of 602P manual (or check the attachment).
Csaba
[
attachment=9969]
It should be noted that the "correct" answer of 2 isn't.
Rounding to different numbers of digits is evil and misleading.
Pauli
Hello!
Could it be, that the FX-602P (don't have one in my collection (yet) so can't try it out myself) has a display formating function similar to "DSP" on the HPs?
When I perform the operation above on an HP-67 (for example) then I will get 2.00 in the default DSP 2 setting wheras it shows 1.999999999 in DSP 9.
And I agree with those who have written above that 2 is not the correct answer. If you calculate the trajectory of a Saturn probe with a calculator (or rather a computer) that comes up with 2 for the square of 1.414213562 then your probe is going to miss Saturn by a very wide margin...
Regards
Max
Thank you all for your input, i learn new things of calculators (casio) here!
So, i comes down to WHEN the casio do the rounding of digits if i get it right?
But, if so, how can fx-4000P, calculate (sqrt 2)^2 to 2?
I just tried it, and i get the result 2.
Isnt the rounding in play here, or has the calculator a table of the right answers in rom?
(10-28-2021 05:33 PM)Steve Simpkin Wrote: [ -> ]This post provides some history of why HP chose not to round off the answers on their calculators.
https://www.hpmuseum.org/forum/thread-17...49274.html
Interesting reading, and examples!
But i'm a bit confused, 1/3+1/3+1/3 gives 1.0 on fx-4000P.
Is that bad or good?
Hello!
(10-28-2021 05:57 PM)Dan C Wrote: [ -> ]But i'm a bit confused, 1/3+1/3+1/3 gives 1.0 on fx-4000P.
Also on the HP-67 (DSP 9) and even on the WP34s.
(10-28-2021 05:57 PM)Dan C Wrote: [ -> ]Is that bad or good?
If the WP34s does it that way it must be good ;-)
Regards
Max
(10-28-2021 06:16 PM)Maximilian Hohmann Wrote: [ -> ]Hello!
(10-28-2021 05:57 PM)Dan C Wrote: [ -> ]But i'm a bit confused, 1/3+1/3+1/3 gives 1.0 on fx-4000P.
Also on the HP-67 (DSP 9) and even on the WP34s.
(10-28-2021 05:57 PM)Dan C Wrote: [ -> ]Is that bad or good?
If the WP34s does it that way it must be good ;-)
Regards
Max
Actually, the 34S returns E-16, which is more correct than 1.
After you do 3 [1/x] [Enter] [Enter] + +, the display shows 1.000000000 (assuming fix 9), but if you then do 1 [-], you'll see the actual result revealed here; it was just hiding due to your display setting.
(10-28-2021 05:32 PM)Dan C Wrote: [ -> ]Thank you all for your input, i learn new things of calculators (casio) here!
So, i comes down to WHEN the casio do the rounding of digits if i get it right?
But, if so, how can fx-4000P, calculate (sqrt 2)^2 to 2?
I just tried it, and i get the result 2.
Isnt the rounding in play here, or has the calculator a table of the right answers in rom?
If you enter \((\sqrt{2})^2-1\) followed by EXE the FX-4000P returns \(-1\times10^{-11}\), which shows that \((\sqrt{2})^2\) is being correctly evaluated as \(1.999\,999\,999\,99\) to 12 significant figures. However, entering \((\sqrt{2})^2\) followed by EXE returns 2 exactly, because of the rounding to 10 significant figures that happens when EXE is pressed.
(Interestingly, the TI-68 calculator allows the user to choose whether pressing ENTER rounds to 10 digits, or whether the full 13-digit precision is retained.)
Nigel (UK)
Wow, i really like the knowledge of calculators on this forum!
Things like if the calculator use 10 or 12 digits, and when and where it does it.
I have now used the fx-4000P a little bit more, making some small programs, and using BASE-n with logical operations etc., and i say as many before me, this must be one of the best calculators ever. beside of the HP's then
.
(10-27-2021 04:23 PM)Dan C Wrote: [ -> ]i tried a simple calculation on 2 of my CASIO, the FX-602P and the fx-4000P.
i did just simply sqrt 2, and then ^2 of the result on both.
FX-602P :
sqrt 2 = 1.414213562
this result ^2 gives 2.
fx-4000P:
sqrt 2 = 1.414213562
this result ^2 gives 1.999999999
I just tried it on my fx 4000 and it also gave 2 ( sqrt 2 EXE , ^2 EXE)
I don't have a real 602P to test with. A 602P emulator on my phone also gave 2 but that does not say anything.