(50g) USER key ": division" a) decimal into (pi) fractions b) no limits

[Gil]

To have handy like on other calculators the

a) conversion from a decimal result
to a (pi) fraction.

Example
7. ENTER
5 :
You get 1.4 in stack 1.

(You could enter also:
'7/5' ENTER —>NUM)

Press then the 3 keys:
LS (white key left to number 4)
Alpha-key (yellow key for USER functions)
: (division key, under TAN key).

You will get
1.4 (in stack level 3)
'7/5' (in stack level 2)
'1+2/5' (in stack level 1).

Code to be entered beforehand:
« —> x
« x TYPE 9 ≠
IF
THEN x DUP DUP
ABS 1 <
IF
THEN —>Q
ELSE —>Q DUP
PROPFRAC
END
ELSE x DUP
PROPFRAC DUP2 SAME
IF
THEN DROP
END
END
»
»

Then add just after the above program the following instructions:
65.1 ASN
(in other words, you asssign this program to key
65.1, i.e. the USER Key .

You can assign afterwards
—>Q¶ (symbol of pi) to 65.2

with the following code
« DUP —>Q¶ »
65.2 ASN

Example
2 ENTER 3 / pi * —>NUM

On stack 1 you should get
2.09439510239.

Now press the 4 keys:
LS (white key left to number 4)
Alpha-key (yellow key for USER functions)
LS (white key left to number 4)
: (division key, under TAN key)

And you get the fraction in function of pi :
'2/3*¶' (Stack 1)
2.09439510239 (decimal value in stack 2).

b) Useful also might be, given a division, to get a lot of decimals :

EXAMPLE
'7/51' ENTER.
It is mandatory to enter the
above expression with
integers only and with
' at the beginning of it
and finish that expression with '
(the relative key ' is the one above the SIN function key).

Press then the 4 keys:
LS (white key left to number 4)
Alpha-key (yellow key for USER functions)
RS (orange key left to number 1)
: (division key, under TAN key).

You should get :
'7/51' (in stack level 3)
.137254901961 (in stack level 2)
13725490196078431372549019607843137254901960784313725490196078431372549019607843​13725490196078431372 (in stack level 1)

To be able to enjoy the above described user 65.3 key,
enter the following code:

« DUPDUP —>NUM SWAP —>STR DUP SIZE RCLF —> x s f
« -105 CF 2 s 1 -
FOR i x "." POS DUP x 1 ROT 1 - SUB x ROT 1 + s SUB + 'x' STO
NEXT x OBJ—> 100 ALOG * PROPFRAC PROPFRAC -105 SF DUP TYPE 9 ==
IF
THEN OBJ—> 3 DROPN
END f STOF
»
»
Then, just after that program, write:
65.3 ASN.

Obervation 1:
You can work on non exact mode and enter for example
'7./5' instead of
'7/5'.

Obervation 2:
As forms like
'7.23/59' are not allowed,
transform them previously into:
'723/59' or '723./59' or
'723/5900' or '723./5900'.

Regards,
Gil