REG x : input

REG 0	: input value x
REG 1	: numerator pk
REG I	: previous numerator pk-1
LBL  3	: entry point
LBL .3	: local label

REG y	: denominator qk
REG x	: numerator pk

Program list

Rev.1.1 Dec. 2 2012

Fractional approximation

001-41,21, 3 LBL 3 002- 36 ENTER 003- 36 ENTER 004- 44 0 STO 0 005- 0 0 006- 44 25 STO I 007- 1 1 008- 44 1 STO 1 009-41,21,.3 LBL .3 010- 33 R↓ 011- 33 R↓ 012- 43 44 INT 013-45,20, 1 RCL× 1 014-45,40,25 RCL+ I 015-42, 4, 1 x<> 1 016- 44 25 STO I 017- 34 x<>y 018- 42 44 FRAC 019- 15 1/x 020- 45 1 RCL 1 021-45,10, 0 RCL÷ 0 022-42, 7, 0 FIX 0 023- 43,34 RND 024-42, 7, 9 FIX 9 025- 36 ENTER 026- 36 ENTER 027- 45 1 RCL 1 028- 31 R/S 029- 10 ÷ 030-42,20, 0 RCL× 0 031- 1 1 032- 30 - 033-43,30, 0 TEST 0 034- 22 .3 GTO .3 035- 34 x<>y 036- 45 1 RCL 1 037- 43 32 RTN

Example

Operation : π GSB C

Result at each R/S

order	0	1	2	3	4
X	3	22	333	355	104348
Y	1	7	106	113	33215

Franctional approximation of π
Fractional approximation program for the HP-32sII
Fractional approximation program for the HP-35S
Fractional approximation program for the HP-42S
Find the nearest fraction in the E24 numbers