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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?
This post provides some history of why HP chose not to round off the answers on their calculators.

(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.

But i'm a bit confused, 1/3+1/3+1/3 gives 1.0 on fx-4000P.
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.
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