Discrepancy between HP 50g and DM42

[PukkaJ]

Hi all,

Today I calculated the energy flux from the sun using the Stefan Bolzmann equation:
EF = sT^4. So as follows:

5777
4
Y^X
5.67E-8
*

On my DM42 and WP34s the result is: 63152788.1436
On my HP 35s and 50g however the result is: 63152788.1439

On my computer Python agrees with my DM42 and WP34s

All display settings were the same on all machines.

What might be causing this difference?

[Joe Horn]

The 35s and 50g (and most other HP models which use BCD math with a 12-digit mantissa) round all intermediate results to 12 significant digits. You'll get the same result on your DM42 if you put it into SCI 11 mode and execute RND after each operation, which is essentially what the 35s and 50g do automatically.

[PukkaJ]

I tried what you suggested and got the same result indeed!

Thank you, I can sleep now!

[berndpr]

Dear PukkaJ,


Because the floating point number in computer are not mathematical real number,
every computer has wrong number at the less significant digits after calculations. Some computer are using additional digits for protection of wrong rounding, but don't use then for displaying. And some not.

I think you has no problem.

You are using a Stefan-Boltzmann constant with only 3 significant digits.
So your result can only have 3 significant digits too, only one more for rounding.

63,2e6 is your answer.

More digits are only pseudo precision without anly information.
I think every science calculator has the right answer.

Bye

[PukkaJ]

(03-12-2021 03:36 AM)berndpr Wrote:  You are using a Stefan-Boltzmann constant with only 3 significant digits.
So your result can only have 3 significant digits too, only one more for rounding.

63,2e6 is your answer.

More digits are only pseudo precision without anly information.
I think every science calculator has the right answer.

This I learned in science class...but sort of forgot and got hung up on high precision calculators!

Thank you very much for reminding me!

[Thomas Okken]

High precision calculators can be useful, because there are calculations that lose digits at the end, like when using poorly-conditioned matrices. When performing calculations like that, the more digits the calculator has, the more valid digits are left at the end, and having a high-precision calculator can make the difference between having a decent number of correct digits, and having no correct digits at all.

But yes, definitely round your final result to have no more digits than your inputs! The extra digits in a high-precision calculator offer a degree of protection against losing digits, but they will never give you any precision that wasn't there to begin with.

[aurelio]

(03-12-2021 07:17 AM)PukkaJ Wrote:  

(03-12-2021 03:36 AM)berndpr Wrote:  You are using a Stefan-Boltzmann constant with only 3 significant digits.
So your result can only have 3 significant digits too, only one more for rounding.

63,2e6 is your answer.

More digits are only pseudo precision without anly information.
I think every science calculator has the right answer.

This I learned in science class...but sort of forgot and got hung up on high precision calculators!

Thank you very much for reminding me!

Thank-you also from me , that remind me my old professor, at that time in laboratory were available only analogic instruments so our habit in tests was to round all our calculations just to the second digit, always the calculator set, so, on FIX2

[PukkaJ]

Just for clarification: 5.67E-8 has 2 decimals in the mantissa, but doesn’t that internally become 0.0000000567 so you really end up with 10 decimals (so you can round the result to a higher precision then when you use say 5.67, all depending on the other parameters involved of course)?

[Albert Chan]

(03-13-2021 01:51 PM)PukkaJ Wrote:  Just for clarification: 5.67E-8 has 2 decimals in the mantissa, but doesn’t that internally become 0.0000000567 ...

Leading zeroes does not count as significant digits.

Stefan-Boltzmann constant, σ = 5.670374419...×10−8 W⋅m−2⋅K−4

Trailing zeroes do count (if it really represent more precision, not just result of scalings)

5.67E-8 is really 5.670E-8, or 4 significant digits.

For an extreme case, 25.4 mm/inch is exact, by definition. The constant has infinite precision.