How does one raise a number to a power in the 9100A?
03-11-2018, 07:29 PM
Post: #1
 zeno333 Member Posts: 189 Joined: Mar 2015
How does one raise a number to a power in the 9100A?
If for example one wanted to do 3^201 on the 9100A how is that done?? By the way, the 9100A was announced to the public 50 years ago today, happy 50th 9100A!
03-11-2018, 07:41 PM (This post was last modified: 03-11-2018 07:46 PM by Dieter.)
Post: #2
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: How does one raise a number to a power in the 9100A?
(03-11-2018 07:29 PM)zeno333 Wrote:  If for example one wanted to do 3^201 on the 9100A how is that done?? By the way, the 9100A was announced to the public 50 years ago today, happy 50th 9100A!

I have never used and not even seen an HP9100 in real life, but since there seems to be no power function you can simply do it the way most later calculators do it internally: yx = ex · ln y.

So in your example you calculate ln 3, multiply this by 201 and finally press ex.

Especially for large results the last digit(s) maybe slightly off, just as on HP calculators with a power key up to the mid-Seventies – these use the same method.

Dieter
03-11-2018, 07:46 PM
Post: #3
 toml_12953 Senior Member Posts: 1,794 Joined: Dec 2013
RE: How does one raise a number to a power in the 9100A?
(03-11-2018 07:29 PM)zeno333 Wrote:  If for example one wanted to do 3^201 on the 9100A how is that done?? By the way, the 9100A was announced to the public 50 years ago today, happy 50th 9100A!

To raise 3 to the 201 power:

3, ln x, R^, 201, *, RV, e^x

where R^ is roll up, RV is roll down and e^x is natural antilog of x (found in left group of keys).

Tom L
Cui bono?
03-11-2018, 07:50 PM (This post was last modified: 03-11-2018 07:57 PM by pier4r.)
Post: #4
 pier4r Senior Member Posts: 2,076 Joined: Nov 2014
RE: How does one raise a number to a power in the 9100A?
From the manual (see mohpc document set. Also nice typeface): would "enter exp" not do the job?

I mean: 3^201 won't change the display, but doing "0+" maybe would do it ?

Update: no, 201 is not available as exponent. As one has two digits only for the exponent. So one has to use exp^(201*ln(3))

Wikis are great, Contribute :)
03-11-2018, 08:16 PM (This post was last modified: 03-11-2018 08:17 PM by toml_12953.)
Post: #5
 toml_12953 Senior Member Posts: 1,794 Joined: Dec 2013
RE: How does one raise a number to a power in the 9100A?
(03-11-2018 07:50 PM)pier4r Wrote:  From the manual (see mohpc document set. Also nice typeface): would "enter exp" not do the job?

I mean: 3^201 won't change the display, but doing "0+" maybe would do it ?

Update: no, 201 is not available as exponent. As one has two digits only for the exponent. So one has to use exp^(201*ln(3))

Even if the calculator used three digits for the exponent, Enter exp wouldn't work. That's only for entering numbers in scientific notation. The base is 10, not 3.
Example (if 9100 allowed three digit exponent)
3, enter exp 201 would give:

3.0000____201

The answer to 3^201 on a 9100 is

7.968 419 671____95

See the difference? They're not even close.

Tom L
Cui bono?
03-11-2018, 08:42 PM
Post: #6
 pier4r Senior Member Posts: 2,076 Joined: Nov 2014
RE: How does one raise a number to a power in the 9100A?
true, exp is base 10. I missed this crucial info looking at the examples.

Wikis are great, Contribute :)
03-11-2018, 08:56 PM (This post was last modified: 03-11-2018 09:08 PM by Dieter.)
Post: #7
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: How does one raise a number to a power in the 9100A?
(03-11-2018 08:42 PM)pier4r Wrote:  true, exp is base 10. I missed this crucial info looking at the examples.

It wouldn't work even if it was any other base. *)

"Enter Exp" simply does the same as the [EEX] key on newer calculators. Guess what EEX stands for. ;-)

Dieter

*) OK, if it was base 3 you could enter 1 [ENTER EXP] 201. #-)
03-11-2018, 09:05 PM (This post was last modified: 03-11-2018 09:14 PM by Dieter.)
Post: #8
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: How does one raise a number to a power in the 9100A?
(03-11-2018 08:16 PM)toml_12953 Wrote:  The answer to 3^201 on a 9100 is

7.968 419 671____95

Very interesting. That's more accurate than the later HP25 where the yx function returns 7,968420280 E+95. The true result is 7,968419666 E+95.
So the 9100 is only +4 ULP off. That's on the same level as the internally 13-digit HP67 (–5 ULP) and HP41 (–2 ULP).

How does the 9100 do it? Is there more than the regular 10-digit accuracy? Could you post the intermediate results, i.e. ln 3, then 201 times this and finally the exponential result?

Dieter
03-11-2018, 09:53 PM
Post: #9
 teenix Senior Member Posts: 1,419 Joined: May 2016
RE: How does one raise a number to a power in the 9100A?
(03-11-2018 08:16 PM)toml_12953 Wrote:  The answer to 3^201 on a 9100 is

7.968 419 671____95

I get that on my 9100B simulator too :-)

cheers

Tony
03-12-2018, 01:19 PM
Post: #10
 pier4r Senior Member Posts: 2,076 Joined: Nov 2014
RE: How does one raise a number to a power in the 9100A?
(03-11-2018 08:56 PM)Dieter Wrote:  "Enter Exp" simply does the same as the [EEX] key on newer calculators. Guess what EEX stands for. ;-)

I mistaken enter exp as y^x, that's it.

Wikis are great, Contribute :)
03-12-2018, 02:28 PM (This post was last modified: 03-12-2018 07:21 PM by toml_12953.)
Post: #11
 toml_12953 Senior Member Posts: 1,794 Joined: Dec 2013
RE: How does one raise a number to a power in the 9100A?
(03-11-2018 09:05 PM)Dieter Wrote:  How does the 9100 do it? Is there more than the regular 10-digit accuracy? Could you post the intermediate results, i.e. ln 3, then 201 times this and finally the exponential result?

Dieter

Here's the calculation in Floating point mode

Code:
                              3        3.    00                            ln       1.098 612 288    00          R^     0.      00                         201     2.01    02                         *        2.01    02                          RV      2.208 210 700    00            e^x    7.968 419 671    95

Tom L
Cui bono?
03-12-2018, 09:31 PM (This post was last modified: 03-12-2018 09:36 PM by Dieter.)
Post: #12
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: How does one raise a number to a power in the 9100A?
(03-12-2018 02:28 PM)toml_12953 Wrote:  Here's the calculation in Floating point mode

Code:
                              3        3.    00                            ln       1.098 612 288    00          R^     0.      00                         201     2.01    02                         *        2.01    02                          RV      2.208 210 700    00            e^x    7.968 419 671    95

Interesting. The ln is slighty low (last digit rounded down instead of up), the multiplication then has a result which is 1 ULP high. Finally the exponentiation is significantly off: e^220,8210700 is 7,968419489 E+95.

So while the result looks very good, it actually is caused by the error of the exponential function which has only 7 correct significant digits. Which only by chance is close to the correct final result.

Dieter
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