Casio FX-602P vs fx-4000P, different results - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: Not HP Calculators (/forum-7.html) +--- Forum: Not remotely HP Calculators (/forum-9.html) +--- Thread: Casio FX-602P vs fx-4000P, different results (/thread-17629.html) Casio FX-602P vs fx-4000P, different results - Dan C - 10-27-2021 04:23 PM 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. RE: Casio FX-602P vs fx-4000P, different results - Nigel (UK) - 10-27-2021 07:33 PM 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) RE: Casio FX-602P vs fx-4000P, different results - Dan C - 10-27-2021 08:21 PM 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. RE: Casio FX-602P vs fx-4000P, different results - Nigel (UK) - 10-27-2021 08:42 PM 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) RE: Casio FX-602P vs fx-4000P, different results - Csaba Tizedes - 10-28-2021 07:32 AM (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] RE: Casio FX-602P vs fx-4000P, different results - Paul Dale - 10-28-2021 08:18 AM It should be noted that the "correct" answer of 2 isn't. Rounding to different numbers of digits is evil and misleading. Pauli RE: Casio FX-602P vs fx-4000P, different results - Maximilian Hohmann - 10-28-2021 02:55 PM 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 RE: Casio FX-602P vs fx-4000P, different results - Dan C - 10-28-2021 05:32 PM 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? RE: Casio FX-602P vs fx-4000P, different results - Steve Simpkin - 10-28-2021 05:33 PM This post provides some history of why HP chose not to round off the answers on their calculators. https://www.hpmuseum.org/forum/thread-17128-post-149274.html RE: Casio FX-602P vs fx-4000P, different results - Dan C - 10-28-2021 05:57 PM (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-17128-post-149274.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? RE: Casio FX-602P vs fx-4000P, different results - Maximilian Hohmann - 10-28-2021 06:16 PM 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 RE: Casio FX-602P vs fx-4000P, different results - rprosperi - 10-28-2021 07:01 PM (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. RE: Casio FX-602P vs fx-4000P, different results - Nigel (UK) - 10-28-2021 09:28 PM (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) RE: Casio FX-602P vs fx-4000P, different results - Dan C - 11-16-2021 08:00 PM 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 . RE: Casio FX-602P vs fx-4000P, different results - johanw - 11-19-2021 08:48 PM (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. RE: Casio FX-602P vs fx-4000P, different results - Csaba Tizedes - 11-19-2021 11:46 PM https://groups.google.com/g/szamologep/c/iEzNlDB_2tc/m/BVy1Ax5ZAgAJ Cs.